Journal articles: 'Group representation theory'

1

Stepanov, S. E. "Group representation theory in relativistic electrodynamics." Russian Physics Journal 39, no. 5 (May 1996): 473–76. http://dx.doi.org/10.1007/bf02436787.

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Steinberg, Benjamin. "Černý’s conjecture and group representation theory." Journal of Algebraic Combinatorics 31, no. 1 (June 2, 2009): 83–109. http://dx.doi.org/10.1007/s10801-009-0185-0.

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Paterson, Alan L. T. "Contractive Representation Theory for the Unitary Group of C(X, M2)." Canadian Journal of Mathematics 39, no. 3 (June 1, 1987): 612–24. http://dx.doi.org/10.4153/cjm-1987-029-0.

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One motivation for studying representation theory for the unitary group of a unital C*-algebra arises from Theoretical Physics. (In the latter connection, Segal [9] and Arveson [1] have developed a representation theory for G. Their approach is in a different direction from ours.) Another motivation for studying the representation theory of G arises out of the desire to unify the theories of amenable von Neumann algebras and amenable locally compact groups.A serious problem for such a representation theory is the absence of Haar measure on G in general.In [7], the author introduced the class RepdG of contractive unitary representations of G, the strong metric condition involved compensating for the lack of Haar measure.

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Gustafson, Paul P. "Finiteness for mapping class group representations from twisted Dijkgraaf–Witten theory." Journal of Knot Theory and Its Ramifications 27, no. 06 (May 2018): 1850043. http://dx.doi.org/10.1142/s0218216518500438.

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We show that any twisted Dijkgraaf–Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image. This generalizes work of Etingof et al. showing that the braid group images are finite [P. Etingof, E. C. Rowell and S. Witherspoon, Braid group representations from twisted quantum doubles of finite groups, Pacific J. Math. 234 (2008)(1) 33–42]. In particular, our result answers their question regarding finiteness of images of arbitrary mapping class group representations in the affirmative. Our approach is to translate the problem into manipulation of colored graphs embedded in the given surface. To do this translation, we use the fact that any twisted Dijkgraaf–Witten representation associated to a finite group [Formula: see text] and 3-cocycle [Formula: see text] is isomorphic to a Turaev–Viro–Barrett–Westbury (TVBW) representation associated to the spherical fusion category [Formula: see text] of twisted [Formula: see text]-graded vector spaces. The representation space for this TVBW representation is canonically isomorphic to a vector space of [Formula: see text]-colored graphs embedded in the surface [A. Kirillov, String-net model of Turaev-Viro invariants, Preprint (2011), arXiv:1106.6033 ]. By analyzing the action of the Birman generators [J. Birman, Mapping class groups and their relationship to braid groups, Comm. Pure Appl. Math. 22 (1969) 213–242] on a finite spanning set of colored graphs, we find that the mapping class group acts by permutations on a slightly larger finite spanning set. This implies that the representation has finite image.

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Häring-Oldenburg, Reinhard. "Braid lift representations of Artin's Braid Group." Journal of Knot Theory and Its Ramifications 09, no. 08 (December 2000): 1005–9. http://dx.doi.org/10.1142/s0218216500000591.

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We recast the braid-lift representation of Contantinescu, Lüdde and Toppan in the language of B-type braid theory. Composing with finite dimensional representations of these braid groups we obtain various sequences of finite dimensional multi-parameter representations.

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Heng Fong, Wan, Aqilahfarhana Abdul Rahman, and Nor Haniza Sarmin. "Isomorphism and matrix representation of point groups." Malaysian Journal of Fundamental and Applied Sciences 15, no. 1 (February 4, 2019): 88–92. http://dx.doi.org/10.11113/mjfas.v15n2019.1087.

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In chemistry, point group is a type of group used to describe the symmetry of molecules. It is a collection of symmetry elements controlled by a form or shape which all go through one point in space, which consists of all symmetry operations that are possible for every molecule. Next, a set of number or matrices which assigns to the elements of a group and represents the multiplication of the elements is said to constitute representation of a group. Here, each individual matrix is called a representative that corresponds to the symmetry operations of point groups, and the complete set of matrices is called a matrix representation of the group. This research was aimed to relate the symmetry in point groups with group theory in mathematics using the concept of isomorphism, where elements of point groups and groups were mapped such that the isomorphism properties were fulfilled. Then, matrix representations of point groups were found based on the multiplication table where symmetry operations were represented by matrices. From this research, point groups of order less than eight were shown to be isomorphic with groups in group theory. In addition, the matrix representation corresponding to the symmetry operations of these point groups wasis presented. This research would hence connect the field of mathematics and chemistry, where the relation between groups in group theory and point groups in chemistry were shown.

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Crumley, Michael. "Generic Representation Theory of the Heisenberg Group." Communications in Algebra 41, no. 8 (August 3, 2013): 3174–206. http://dx.doi.org/10.1080/00927872.2012.683908.

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Daugherty, Zajj, Alexander K. Eustis, Gregory Minton, and Michael E. Orrison. "Voting, the Symmetric Group, and Representation Theory." American Mathematical Monthly 116, no. 8 (October 1, 2009): 667–87. http://dx.doi.org/10.4169/193009709x460796.

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9

CRANE, LOUIS. "STRING FIELD THEORY FROM QUANTUM GRAVITY." Reviews in Mathematical Physics 25, no. 10 (November 2013): 1343005. http://dx.doi.org/10.1142/s0129055x13430058.

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Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) representations is just the dual model on the extended lattice of the Lie group E6, as explained by the quantum McKay correspondence of Frenkel, Jing and Wang. The coupled model can be thought of as string field theory, but propagating on a discretized quantum spacetime rather than a classical manifold.

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10

ZHENG, H. "A REFLEXIVE REPRESENTATION OF BRAID GROUPS." Journal of Knot Theory and Its Ramifications 14, no. 04 (June 2005): 467–77. http://dx.doi.org/10.1142/s0218216505003877.

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In this paper, for every positive integer m, we define a representation ξn,m of the n-strand braid group Bn over a free ℤBn+m-module. It not only provides an approach to construct new representations of braid groups, but also gives a new perspective to the homological representations such as the Lawrence–Krammer representation.

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Spitzer, Aaron John. "Reconciling Shared Rule: Liberal Theory, Electoral-Districting Law and “National Group” Representation in Canada." Canadian Journal of Political Science 51, no. 2 (February 19, 2018): 447–66. http://dx.doi.org/10.1017/s0008423918000033.

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AbstractCanada, like all representative democracies, apportions representation to individuals; also, like all federal states, it accords polity-based representation to federal subunits. But Canada is additionally a consociational state, comprising three constitutionally recognized “national groups”: anglophones, francophones and Indigenous peoples. These groups share power and bear rights beyond the bounds of the federal system. In recent decades, Indigenous peoples and francophones have appealed for representation as “national groups,” leading to constitutional challenges. Courts have either failed to address the constitutionality of “national group” representation or have rejected it as irreconcilable with individual voting rights. I suggest the former is unnecessary and the latter procedurally illogical. Drawing on the liberal principles of individualism, egalitarianism and universalism, I develop a framework contextualizing such representation within liberal theory. I then deploy this framework to analyze recent Canadian case law. I show that appeals for “national group” representation should be approached not through the lens of individual rights, but rather through the “constitutionally prior” lens of universalism.

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12

CHEN, SI. "MAPPING CLASS GROUP AND U(1) CHERN–SIMONS THEORY ON CLOSED ORIENTABLE SURFACES." Modern Physics Letters A 27, no. 15 (May 15, 2012): 1250087. http://dx.doi.org/10.1142/s0217732312500873.

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U(1) Chern–Simons theory is quantized canonically on manifolds of the form [Formula: see text], where Σ is a closed orientable surface. In particular, we investigate the role of mapping class group of Σ in the process of quantization. We show that, by requiring the quantum states to form representation of the holonomy group and the large gauge transformation group, both of which are deformed by quantum effect, the mapping class group can be consistently represented, provided the Chern–Simons parameter k satisfies an interesting quantization condition. The representations of all the discrete groups are unique, up to an arbitrary sub-representation of the mapping class group. Also, we find a k↔1/k duality of the representations.

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13

NARUSE, Hiroshi. "Representation Theory of Weyl Group of Type $C_n$." Tokyo Journal of Mathematics 08, no. 1 (June 1985): 177–90. http://dx.doi.org/10.3836/tjm/1270151578.

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14

Boisen, Paul R. "The representation theory of fully group-graded algebras." Journal of Algebra 151, no. 1 (September 1992): 160–79. http://dx.doi.org/10.1016/0021-8693(92)90137-b.

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15

Cen, Li-Xiang, Xin-Qi Li, and Yi Jing Yan. "Characterization of entanglement transformation via group representation theory." Journal of Physics A: Mathematical and General 36, no. 49 (November 26, 2003): 12267–73. http://dx.doi.org/10.1088/0305-4470/36/49/009.

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16

Constantinescu, F., and F. Toppan. "On the Linearized Artin Braid Representation." Journal of Knot Theory and Its Ramifications 02, no. 04 (December 1993): 399–412. http://dx.doi.org/10.1142/s0218216593000222.

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We linearize the Artin representation of the braid group given by (right) automorphisms of a free group providing a linear faithful representation of the braid group. This result is generalized to obtain linear representations for the coloured braid groupoid and pure braid group too. Applications to some areas of two-dimensional physics are mentioned.

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REINEKE, MARCUS. "THE MONOID OF FAMILIES OF QUIVER REPRESENTATIONS." Proceedings of the London Mathematical Society 84, no. 3 (April 29, 2002): 663–85. http://dx.doi.org/10.1112/s0024611502013497.

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A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, that is, subvarieties of the varieties of representations. The study of this monoid leads to interesting interactions between representation theory, algebraic geometry and quantum group theory. For example, it produces a wealth of interesting examples of families of quiver representations, which can be analysed by representation-theoretic and geometric methods. Conversely, results from representation theory, in particular A. Schofield's work on general properties of quiver representations, allow us to relate the monoid to certain degenerate forms of quantized enveloping algebras.2000 Mathematical Subject Classification: 16G20, 14L30, 17B37.

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18

Celis, Karen, and Liza M. Mügge. "Whose equality? Measuring group representation." Politics 38, no. 2 (January 30, 2017): 197–213. http://dx.doi.org/10.1177/0263395716684527.

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Presence, of bodies and ideas, is often taken as the primary indicator of political equality and, hence, democratic health. Intersectionality and constructivism question the validity of measuring presence. Turning theory into practice, we propose a comparative reflexive design guided by two research questions: (1) Who are the groups? and (2) What are their problems? This reveals both prototypical and non-prototypical groups and interests, from the perspectives of politicians (from above) and citizens (from below). We suggest concrete qualitative and quantitative methodological strategies to study these questions empirically.

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19

Moran, Alan. "The Right Regular Representation of a Compact Right Topological Group." Canadian Mathematical Bulletin 41, no. 4 (December 1, 1998): 463–72. http://dx.doi.org/10.4153/cmb-1998-060-2.

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AbstractWe show that for certain compact right topological groups, , the strong operator topology closure of the image of the right regular representation of G in L(H), where H = L2(G), is a compact topological group and introduce a class of representations, R , which effectively transfers the representation theory of over to G. Amongst the groups for which this holds is the class of equicontinuous groups which have been studied by Ruppert in [10].We use familiar examples to illustrate these features of the theory and to provide a counter-example. Finally we remark that every equicontinuous group which is at the same time a Borel group is in fact a topological group.

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DADARLAT, MARIUS. "GROUP QUASI-REPRESENTATIONS AND INDEX THEORY." Journal of Topology and Analysis 04, no. 03 (September 2012): 297–319. http://dx.doi.org/10.1142/s1793525312500148.

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Let M be a closed connected manifold and let D be an elliptic operator on M. Let G be a discrete countable group and let [Formula: see text] be a principal G-bundle. Connes and Moscovici showed that this data defines an analytic index ind ℓ1(G)(D) ∈ K0(ℓ1(G)). If B is a unital tracial C*-algebra, we give a formula for the trace of the image of ind ℓ1(G)(D) in K0(B) under the map induced by a quasi-representation of G in B. As an application, we reprove and generalize a formula of Exel and Loring to surface groups.

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21

Wang, Yilong. "Modular group representations associated to SO(p)2-TQFTS." Journal of Knot Theory and Its Ramifications 28, no. 05 (April 2019): 1950037. http://dx.doi.org/10.1142/s0218216519500378.

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In this paper, we prove that for any odd prime [Formula: see text] greater than 3, the modular group representation associated to the [Formula: see text]-topological quantum field theory can be defined over the ring of integers of a cyclotomic field. We will provide explicit integral bases. In the last section, we will relate these representations to the Weil representations over finite fields.

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22

Proctor, Robert A. "A Schensted Algorithm Which Models Tensor Representations of the Orthogonal Group." Canadian Journal of Mathematics 42, no. 1 (February 1, 1990): 28–49. http://dx.doi.org/10.4153/cjm-1990-002-1.

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This paper is concerned with a combinatorial construction which mysteriously “mimics” or “models” the decomposition of certain reducible representations of orthogonal groups. Although no knowledge of representation theory is needed to understand the body of this paper, a little familiarity is necessary to understand the representation theoretic motivation given in the introduction. Details of the proofs will most easily be understood by people who have had some exposure to Schensted's algorithm or jeu de tacquin.

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23

WRIGHT, GRETCHEN. "THE RESHETIKHIN-TURAEV REPRESENTATION OF THE MAPPING CLASS GROUP AT THE SIXTH ROOT OF UNITY." Journal of Knot Theory and Its Ramifications 05, no. 05 (October 1996): 721–39. http://dx.doi.org/10.1142/s0218216596000412.

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The quantum group construction of Reshetikhin and Turaev provides representations of the mapping class group, indexed by an integer parameter r. This paper presents computations of these representations when r=6, and analyzes their relationship to other topological invariants. It is shown that in genus 2, the representation splits into two summands. The first summand factors through the mapping class group action on the first homology of the surface with Z/3Z coefficients, while the second summand can be analyzed via its restriction to the subgroup of the mapping class group which is normally generated by the sixth power of a Dehn twist on a nonseparating curve. This analysis reveals a connection to the homology intersection pairing on the surface, and also yields information about the kernel and image of the representation. It is also shown that the representation yields a family of 2-dimensional nonabelian representations of the Torelli group. This paper continues the program established by the author in [Wr] to relate the Reshetikhin-Turaev representations at specific roots of unity to classical invariants.

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PATTANAYAK, S. K. "ON SOME STANDARD GRADED ALGEBRAS IN MODULAR INVARIANT THEORY." Journal of Algebra and Its Applications 13, no. 01 (August 20, 2013): 1350080. http://dx.doi.org/10.1142/s0219498813500801.

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For a finite-dimensional representation V of a finite group G over a field K we denote the graded algebra R ≔ ⨁d≥0 Rd; where Rd ≔ ( Sym d∣G∣V*)G. We study the standardness of R for the representations [Formula: see text], [Formula: see text], and [Formula: see text], where Vn denote the n-dimensional indecomposable representation of the cyclic group Cp over the Galois field 𝔽p, for a prime p. We also prove the standardness for the defining representation of all finite linear groups with polynomial rings of invariants. This is motivated by a question of projective normality raised in [S. S. Kannan, S. K. Pattanayak and P. Sardar, Projective normality of finite groups quotients, Proc. Amer. Math. Soc.137(3) (2009) 863–867].

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ABDULRAHIM, MOHAMMAD N. "PURE BRAIDS AS AUTOMORPHISMS OF FREE GROUPS." Journal of Algebra and Its Applications 04, no. 04 (August 2005): 435–40. http://dx.doi.org/10.1142/s0219498805001277.

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We study the composition of F. R. Cohen's map Pn → Pnk with the Gassner representation, where Pn is the pure braid group. This gives us a linear representation of Pn whose composition factors are one copy of the Gassner representation of Pn and k - 1 copies of a diagonal representation, hence a direct sum of one-dimensional representations.

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26

West, Peter. "Irreducible representations of E theory." International Journal of Modern Physics A 34, no. 24 (August 29, 2019): 1950133. http://dx.doi.org/10.1142/s0217751x19501331.

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We construct the [Formula: see text] theory analogue of the particles that transform under the Poincaré group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of [Formula: see text] with its vector representation. We show that one such irreducible representation has only the degrees of freedom of 11-dimensional supergravity. This representation is most easily discussed in the light cone formalism and we show that the duality relations found in [Formula: see text] theory take a particularly simple form in this formalism. We explain that the mysterious symmetries found recently in the light cone formulation of maximal supergravity theories are part of [Formula: see text]. We also argue that our familiar space–times have to be extended by additional coordinates when considering extended objects such as branes.

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EGEA, CLAUDIA MARÍA, and ESTHER GALINA. "SOME IRREDUCIBLE REPRESENTATIONS OF THE BRAID GROUP 𝔹n OF DIMENSION GREATER THAN n." Journal of Knot Theory and Its Ramifications 19, no. 04 (April 2010): 539–46. http://dx.doi.org/10.1142/s0218216510007966.

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For any n ≥ 3, we construct a family of finite-dimensional irreducible representations of the braid group 𝔹n. Moreover, we give necessary conditions for a member of this family to be irreducible. In particular we give a explicitly irreducible subfamily (ϕm, Vm), 1 ≤ m < n, where [Formula: see text]. The representation obtained in the case m = 1 is equivalent to the standard representation.

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LIVINGSTON, CHARLES. "LIFTING REPRESENTATIONS OF KNOT GROUPS." Journal of Knot Theory and Its Ramifications 04, no. 02 (June 1995): 225–34. http://dx.doi.org/10.1142/s0218216595000120.

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Given a representation of a classical knot group onto a quotient group E/A, we address the classification of lifts of that representation onto E. The classification is given first in terms of classical obstruction theory and then, in many cases, interpreted in terms of the homology of covers of the knot complement. Applications include the study of dihedral, metacyclic, and metabelian representations. Properties of the restrictions of lifts to the peripheral subgroup are also studied.

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Saeed, Muhammad Sarwar, Muhammad Ashiq, Tariq Alraqad, and Tahir Imran. "PERMUTATION REPRESENTATION OF A TRIANGLE GROUP." JP Journal of Algebra, Number Theory and Applications 44, no. 2 (November 10, 2019): 159–80. http://dx.doi.org/10.17654/nt044020159.

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30

Mangum, Brian, and Patrick Shanahan. "Three-Dimensional Representations of Punctured Torus Bundles." Journal of Knot Theory and Its Ramifications 06, no. 06 (December 1997): 817–25. http://dx.doi.org/10.1142/s0218216597000455.

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In this paper, we construct a complex curve of irreducible [Formula: see text] representations of the fundamental group of a once punctured torus bundle over the circle. These representations are different from those obtained by composing representations in [Formula: see text] with the unique irreducible representation of [Formula: see text] in [Formula: see text]. Moreover, infinitely many of these representations are conjugate to SU(3) representations. We conclude the paper with a computation of the curve in the case that the bundle is the figure-eight knot complement, and we show that for infinitely many Dehn surgeries on the figure-eight knot, there is a representation from this curve that descends to a representation of the fundamental group of the surgered manifold.

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31

Gross, Benedict H. "Representation theory and the cuspidal group of $X(p)$." Duke Mathematical Journal 54, no. 1 (1987): 67–75. http://dx.doi.org/10.1215/s0012-7094-87-05406-8.

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32

Popov, V. S. "Feynman disentangling of noncommuting operators and group representation theory." Physics-Uspekhi 50, no. 12 (December 31, 2007): 1217–38. http://dx.doi.org/10.1070/pu2007v050n12abeh006401.

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Popov, Vladimir S. "Feynman disentangling оf noncommuting operators and group representation theory." Uspekhi Fizicheskih Nauk 177, no. 12 (2007): 1319. http://dx.doi.org/10.3367/ufnr.0177.200712f.1319.

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de la Iglesia, Manuel D., and Pablo Román. "Some bivariate stochastic models arising from group representation theory." Stochastic Processes and their Applications 128, no. 10 (October 2018): 3300–3326. http://dx.doi.org/10.1016/j.spa.2017.10.017.

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Akin, Kaan, and David A. Buchsbaum. "Characteristic-free representation theory of the general linear group." Advances in Mathematics 58, no. 2 (November 1985): 149–200. http://dx.doi.org/10.1016/0001-8708(85)90115-x.

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Asmuth, C. "An application of group representation theory to picture recognition." Computers & Mathematics with Applications 13, no. 4 (1987): 363–65. http://dx.doi.org/10.1016/0898-1221(87)90003-4.

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EHOLZER, W. "FUSION ALGEBRAS INDUCED BY REPRESENTATIONS OF THE MODULAR GROUP." International Journal of Modern Physics A 08, no. 20 (August 10, 1993): 3495–507. http://dx.doi.org/10.1142/s0217751x93001405.

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Using the representation theory of the subgroups SL 2(ℤp) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to "good" fusion algebras. Furthermore, the conformal dimensions and the central charge of the corresponding rational conformal field theories are calculated. Two series of representations which can be realized by unitary theories are presented. We show that most of the fusion algebras induced by admissible representations are realized in well-known rational models.

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Hivert, Florent, and Nicolas M. Thiéry. "The Hecke group algebra of a Coxeter group and its representation theory." Journal of Algebra 321, no. 8 (April 2009): 2230–58. http://dx.doi.org/10.1016/j.jalgebra.2008.09.039.

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39

Kornyak, Vladimir. "Modeling Quantum Behavior in the Framework of Permutation Groups." EPJ Web of Conferences 173 (2018): 01007. http://dx.doi.org/10.1051/epjconf/201817301007.

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Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite group can be realized as a subrepresentation of a permutation representation. Thus, quantum-mechanical problems can be expressed in terms of permutation groups. This approach allows us to clarify the meaning of a number of physical concepts. Combining methods of computational group theory with Monte Carlo simulation we study a model based on representations of permutation groups.

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DE JEU, MARCEL, and MARTEN WORTEL. "POSITIVE REPRESENTATIONS OF FINITE GROUPS IN RIESZ SPACES." International Journal of Mathematics 23, no. 07 (June 27, 2012): 1250076. http://dx.doi.org/10.1142/s0129167x12500760.

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In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite-dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. We describe the finite-dimensional positive Archimedean representations of a finite group and establish that, up to order equivalence, these are order direct sums, with unique multiplicities, of the order indecomposable positive representations naturally associated with transitive G-spaces. Character theory is shown to break down for positive representations. Induction and systems of imprimitivity are introduced in an ordered context, where the multiplicity formulation of Frobenius reciprocity turns out not to hold.

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Bellaïche, Joël, and Gaëtan Chenevier. "The sign of Galois representations attached to automorphic forms for unitary groups." Compositio Mathematica 147, no. 5 (July 27, 2011): 1337–52. http://dx.doi.org/10.1112/s0010437x11005264.

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AbstractLet K be a CM number field and GK its absolute Galois group. A representation of GK is said to be polarized if it is isomorphic to the contragredient of its outer complex conjugate, up to a twist by a power of the cyclotomic character. Absolutely irreducible polarized representations of GK have a sign ±1, generalizing the fact that a self-dual absolutely irreducible representation is either symplectic or orthogonal. If Π is a regular algebraic, polarized, cuspidal automorphic representation of GLn(𝔸K), and if ρ is a p-adic Galois representation attached to Π, then ρ is polarized and we show that all of its polarized irreducible constituents have sign +1 . In particular, we determine the orthogonal/symplectic alternative for the Galois representations associated to the regular algebraic, essentially self-dual, cuspidal automorphic representations of GLn (𝔸F) when F is a totally real number field.

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Pavlov, A. M. "Group-Theoretical Analysis of the Clustered Launch Vehicle Dynamics." Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, no. 4 (127) (August 2019): 20–30. http://dx.doi.org/10.18698/0236-3941-2019-4-20-30.

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In this paper we considered representation-theory-based eigenfunction classification of clustered launch vehicles vibration problems. Classification of vibrations modes was obtained by using projection operators, related with corresponding subspaces of irreducible representations of considered mechanical system symmetry group. For multiple frequencies we proposed the approach which allows to reduce corresponding vibrations modes to launch vehicle stabilization planes. In addition, for the launch vehicle with four boosters, the projections onto irreducible representations subspaces of right-hand side of the motion equations were found.

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DOBREV, V. K. "NONRELATIVISTIC HOLOGRAPHY — A GROUP-THEORETICAL PERSPECTIVE." International Journal of Modern Physics A 29, no. 03n04 (February 10, 2014): 1430001. http://dx.doi.org/10.1142/s0217751x14300014.

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We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall the interpretation of nonrelativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. One important result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory, and that these operators and the bulk-to-boundary operators are intertwining operators. Further, we recall the fact that there is a hierarchy of equations on the boundary, invariant with respect to Schrödinger algebra. We also review the explicit construction of an analogous hierarchy of invariant equations in the bulk, and that the two hierarchies are equivalent via the bulk-to-boundary intertwining operators. The derivation of these hierarchies uses a mechanism introduced first for semisimple Lie groups and adapted to the nonsemisimple Schrödinger algebra. These require development of the representation theory of the Schrödinger algebra which is reviewed in some detail. We also recall the q-deformation of the Schrödinger algebra. Finally, the realization of the Schrödinger algebra via difference operators is reviewed.

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SILVER, DANIEL S., and SUSAN G. WILLIAMS. "ON A THEOREM OF BURDE AND DE RHAM." Journal of Knot Theory and Its Ramifications 20, no. 05 (May 2011): 713–20. http://dx.doi.org/10.1142/s0218216511008917.

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We generalize a theorem of Burde and de Rham characterizing the zeros of the Alexander polynomial. Given a representation of a knot group π, we define an extension [Formula: see text] of π, the Crowell group. For any GL Nℂ representation of π, the zeros of the associated twisted Alexander polynomial correspond to representations of [Formula: see text] into the group of dilations of ℂN.

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Araújo, Ivonete Alves de, Ana Beatriz Azevedo Queiroz, Maria Aparecida Vasconcelos Moura, and Lúcia Helena Garcia Penna. "Social representations of the sexual life of climacteric women assisted at public health services." Texto & Contexto - Enfermagem 22, no. 1 (March 2013): 114–22. http://dx.doi.org/10.1590/s0104-07072013000100014.

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The present study aimed at studying the social representations of the sexual life of climacteric women. Its theoretical-methodological referential was based on the Theory of Social Representations. Study participants were 40 women between 45 and 65 years of age, who were divided into two groups: perimenopause and postmenopause. Scenarios were two public units of health services for women in the municipality of Rio de Janeiro. Data were collected through the semistructured interview technique and treated according to the analysis of thematic content. Results indicated three representation fields. Two fields emerged in the perimenopause group: continuity of sensuality and sexuality, and representation of the negativity in climacteric leading to a sexual life without pleasure. The postmenopause group was organized into one representational field: sexual life based on the aging process. The authors concluded that the representations regarding sexual life in climacteric are being redesigned by some women despite many conceptions that still persist in association with traditional socio-historical-cultural values regarding women and the aging process.

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ABDULRAHIM, MOHAMMAD N. "ON THE COMPOSITION OF THE BURAU REPRESENTATION AND THE NATURAL MAP Bn → Bnk." Journal of Algebra and Its Applications 02, no. 02 (June 2003): 169–75. http://dx.doi.org/10.1142/s0219498803000465.

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A lot of linear representations of the braid group, Bn, arise as a result of treating braids as automorphisms of a free group. In this paper, we consider the composition of F. R. Cohen's map Bn → Bnk and the embedding Bnk → Aut (Fnk). This gives us a linear representation of Bn whose composition factors are one copy of the Burau representation and k - 1 copies of the standard representation, a representation investigated by I. Sysoeva.

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LANDSMAN, N. P. "QUANTIZATION AND SUPERSELECTION SECTORS I: TRANSFORMATION GROUP C*-ALGEBRAS." Reviews in Mathematical Physics 02, no. 01 (January 1990): 45–72. http://dx.doi.org/10.1142/s0129055x9000003x.

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Quantization is defined as the act of assigning an appropriate C*-algebra [Formula: see text] to a given configuration space Q, along with a prescription mapping self-adjoint elements of [Formula: see text] into physically interpretable observables. This procedure is adopted to solve the problem of quantizing a particle moving on a homogeneous locally compact configuration space Q=G/H. Here [Formula: see text] is chosen to be the transformation group C*-algebra corresponding to the canonical action of G on Q. The structure of these algebras and their representations are examined in some detail. Inequivalent quantizations are identified with inequivalent irreducible representations of the C*-algebra corresponding to the system, hence with its superselection sectors. Introducing the concept of a pre-Hamiltonian, we construct a large class of G-invariant time-evolutions on these algebras, and find the Hamiltonians implementing these time-evolutions in each irreducible representation of [Formula: see text]. “Topological” terms in the Hamiltonian (or the corresponding action) turn out to be representation-dependent, and are automatically induced by the quantization procedure. Known “topological” charge quantization or periodicity conditions are then identically satisfied as a consequence of the representation theory of [Formula: see text].

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Rodrigues Jacinto, Joaquín, and Juan Rodríguez Camargo. "Solid locally analytic representations of 𝑝-adic Lie groups." Representation Theory of the American Mathematical Society 26, no. 31 (August 31, 2022): 962–1024. http://dx.doi.org/10.1090/ert/615.

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We develop the theory of locally analytic representations of compact p p -adic Lie groups from the perspective of the theory of condensed mathematics of Clausen and Scholze. As an application, we generalise Lazard’s isomorphisms between continuous, locally analytic and Lie algebra cohomology to solid representations. We also prove a comparison result between the group cohomology of a solid representation and of its analytic vectors.

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DELBOURGO, DANIEL, and PAUL SMITH. "Kummer theory for big Galois representations." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 2 (March 2007): 205–17. http://dx.doi.org/10.1017/s0305004106009868.

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AbstractIn their 1990 paper, Bloch and Kato described the image of the Kummer map on an abelian variety over a local field, as the group of 1-cocycles which trivialise after tensoring by Fontaine's mysterious ring BdR. We prove the analogue of this statement for the universal nearly-ordinary Galois representation. The proof uses a generalisation of the Tate local pairing to representations over affinoid K-algebras.

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BARDAKOV, VALERIJ G. "EXTENDING REPRESENTATIONS OF BRAID GROUPS TO THE AUTOMORPHISM GROUPS OF FREE GROUPS." Journal of Knot Theory and Its Ramifications 14, no. 08 (December 2005): 1087–98. http://dx.doi.org/10.1142/s0218216505004251.

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We construct a linear representation of the group IA (Fn) of IA-automorphisms of a free group Fn, an extension of the Gassner representation of the pure braid group Pn. Although the problem of faithfulness of the Gassner representation is still open for n > 3, we prove that the restriction of our representation to the group of basis conjugating automorphisms Cbn contains a non-trivial kernel even if n = 2. We construct also an extension of the Burau representation to the group of conjugating automorphisms Cn. This representation is not faithful for n ≥ 2.

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Journal articles on the topic 'Group representation theory'

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