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Dissertations / Theses on the topic 'Lorentz groups. Representations of groups'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Evseeva, Elena. "Représentations du groupe pseudo-orthogonal dans les espaces des formes différentielles homogènes." Thesis, Reims, 2016. http://www.theses.fr/2016REIMS035/document.

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Dans cette thèse nous étudions des représentations du groupe de Lorentz dans les sections du fibré cotangent sur le cône isotrope. Grâce aux transformations de Fourier et de Poisson nous construisons explicitement tous les opérateurs de brisure de symétrie qui apparaissent dans les lois de branchement des produits tensoriels de telles représentations<br>In this thesis we study representations of the Lorentz group acting on sectionsof the cotangent bundle over the isotropic cone. Using Fourier and Poisson transforms we construct explicitly all the symmetry breaking operators that appear in bran

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2

Sjöstedt, Klas. "The 2+1 Lorentz Group and Its Representations." Thesis, Stockholms universitet, Fysikum, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-183368.

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The Lorentz group is a symmetry group on Minkowski space, and as such is central to studying the geometry of this and related spaces. The group therefore shows up also from physical considerations, such as trying to formulate quantum physics in anti-de Sitter space. In this thesis, the Lorentz group in 2+1 dimensions and its representations are investigated, and comparisons are made to the analogous rotation group. Firstly, all unitary irreducible representations are found and classiﬁed. Then, those representations are realised as the square-integrable, analytic functions on the unit circle an

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3

Andrus, Ivan B. "Matrix Representations of Automorphism Groups of Free Groups." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd856.pdf.

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4

Hannesson, Sigurdur. "Representations of symmetric groups." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442464.

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5

Stavis, Andreas. "Representations of finite groups." Thesis, Karlstads universitet, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-69642.

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Representation theory is concerned with the ways of writing elements of abstract algebraic structures as linear transformations of vector spaces. Typical structures amenable to representation theory are groups, associative algebras and Lie algebras. In this thesis we study linear representations of finite groups. The study focuses on character theory and how character theory can be used to extract information from a group. Prior to that, concepts needed to treat character theory, and some of their ramifications, are investigated. The study is based on existing literature, with excessive use of

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6

Scopes, Joanna. "Representations of the symmetric groups." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279989.

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7

Lawrence, Ruth Jayne. "Homology representations of braid groups." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236125.

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8

Towers, Matthew John. "Modular representations of p-groups." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427611.

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9

Can, Himmet. "Representations of complex reflection groups." Thesis, Aberystwyth University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289795.

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10

Cai, Yuanqing. "Theta representations on covering groups." Thesis, Boston College, 2017. http://hdl.handle.net/2345/bc-ir:107492.

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Thesis advisor: Solomon Friedberg<br>Kazhdan and Patterson constructed generalized theta representations on covers of general linear groups as multi-residues of the Borel Eisenstein series. For the double covers, these representations and their (degenerate-type) unique models were used by Bump and Ginzburg in the Rankin-Selberg constructions of the symmetric square L-functions for GL(r). In this thesis, we study two other types of models that the theta representations may support. We first discuss semi-Whittaker models, which generalize the models used in the work of Bump and Ginzburg. Secondl

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11

Wildon, Mark. "Modular representations of symmetric groups." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403775.

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12

Iano-Fletcher, Maria. "Polynomial representations of symplectic groups." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/89157/.

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In Chapter 1 we review some of the classical theory of reductive algebraic groups over an algebraically closed field. In Chapter 2 we summarise the work of Green on polynomial representations of GLn(k) where k is an infinite field. The irreducible polynomial representations of degree r of GLn(k) are parametrised by partitions λ of r. The irreducible polynomial GLn(k)-module F λ k can be obtained in two ways, as the quotient of a Weyl module V λ k by its unique maximal submodule, or as the unique minimal submodule of a Shur module D λ k. The two modules V λ k and D λ k are duals of one another.

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13

Hindeleh, Firas. "Tangent and cotangent bundles automorphism groups and representations of Lie groups /." See Full Text at OhioLINK ETD Center (Requires Adobe Acrobat Reader for viewing), 2006. http://www.ohiolink.edu/etd/view.cgi?acc_num=toledo1153933389.

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Thesis (Ph.D.)--University of Toledo, 2006.<br>Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 79-82.

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14

Kielak, Dawid. "Free and linear representations of outer automorphism groups of free groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:f2045fba-1546-4dd3-af9f-7d02c4fc505e.

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For various values of n and m we investigate homomorphisms from Out(F_n) to Out(F_m) and from Out(F_n) to GL_m(K), i.e. the free and linear representations of Out(F_n) respectively. By means of a series of arguments revolving around the representation theory of finite symmetric subgroups of Out(F_n) we prove that each homomorphism from Out(F_n) to GL_m(K) factors through the natural map p_n from Out(F_n) to GL(H_1(F_n,Z)) = GL_n(Z) whenever n=3, m < 7 and char(K) is not an element of {2,3}, and whenever n>5, m< n(n+1)/2 and char(K) is not an element of {2,3,...,n+1}. We also construct a new in

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15

Hindeleh, Firas Y. "Tangent and Cotangent Bundles, Automorphism Groups and Representations of Lie Groups." University of Toledo / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1153933389.

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16

Szechtman, Fernando. "Weil representations of finite symplectic groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0006/NQ39598.pdf.

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17

Quinlan, Rachel. "Irreducible projective representations of finite groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ59658.pdf.

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18

Benjamin, Ian Francis. "Quasi-permutation representations of finite groups." Thesis, University of Liverpool, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250561.

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19

Martin, Benjamin Michael Sinclair. "Varieties of representations of surface groups." Thesis, King's College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243429.

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20

Nabney, Ian Thomas. "Soluble minimax groups and their representations." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333316.

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21

Mason-Brown, Lucas(Lucas David). "Unipotent representations of real reductive groups." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/126931.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020<br>Cataloged from the official PDF of thesis.<br>Includes bibliographical references (pages 207-210).<br>Let G be a real reductive group and let Ĝ be the set of irreducible unitary representations of G. The determination of Ĝ (for arbitrary G) is one of the fundamental unsolved problems in representation theory. In the early 1980s, Arthur introduced a finite set Unip(G) of (conjecturally unitary) irreducible representations of G called unipotent representations. In a certain sense, these representations

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22

Ronquillo, Rivera Javier Alfredo. "Extremely Amenable Groups and Banach Representations." Ohio University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520548085599864.

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23

Anwar, Muhammad F. "Representations and cohomology of algebraic groups." Thesis, University of York, 2011. http://etheses.whiterose.ac.uk/2032/.

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Let G be a semisimple simply connected linear algebraic group over an algebraically closed field k of characteristic p. In [11], Donkin gave a recursive description for the characters of cohomology of line bundles on the flag variety G/B with G = SL3. In chapter 2 of this thesis we try to give a non recursive description for these characters. In chapter 3, we give the first step of a version of formulae in [11] for G = G2. In his famous paper [7], Demazure introduced certain indecomposable modules and used them to give a short proof of the Borel-Weil-Bott theorem (characteristic zero). In chap

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24

Sun, Binyong. "Matrix coefficients and representations of real reductive groups /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20SUN.

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25

Nguyen, Benny. "Symmetrically generated groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2902.

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This thesis constructs several groups entirely by hand via their symmetric presentations. In particular, the technique of double coset enumeration is used to manually construct J₃ : 2, the automorphism group of the Janko group J₃, and represent every element of the group as a permutation of PSL₂ (16) : 4, on 120 letters, followed by a word of length at most 3.

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26

Girard, Réjean. "Relativistic nonlinear wave equations with groups of internal symmetry." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75688.

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A nonlinear wave equation invariant with respect to unitary representations of the Lorentz group is considered in an attempt to describe extended particles with spin and positive definite energy by means of a self-confined classical field. The wave function has an infinite number of components and, in the specific representations used, the corresponding internal degree of freedom is identified with the spin. A fractional power of the scalar bilinear invariant appears as an appropriate choice for the nonlinearity in order that all the stationary states be localized. Two approximation methods ar

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27

Fairley, Jason Thomas. "Induced linear representations for doubly transitive groups." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.404812.

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28

Forrester-Barker, Magnus. "Representations of crossed modules and catÂ¹-groups." Thesis, Bangor University, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401882.

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29

Almutairi, Bander Nasser. "Counting supercuspidal representations of p-adic groups." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/48008/.

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Let F be a non-archimedean local �eld with residual characteristic p ~= 2. In this thesis we will deduce a formula for the number of irreducible supercuspidal representations of GLN(F), N C 1, with !�($F ) = 1 and level less than or equal to k. Following Blasco, we construct all irreducible supercuspidal representations of the unitary groups U(1; 1)(F~F0) and U(2; 1)(F~F0) by looking at their characteristic polynomials and then compute the number of all these representations according to their level.

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30

Magson, Christopher. "Real projective representations of some finite groups." Thesis, University of Liverpool, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236595.

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31

AFONSO, LUIS FERNANDO CROCCO. "REPRESENTATIONS OF TRIANGLE GROUPS IN COMPLEX HYPERBOLIC." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4123@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>O principal objetivo deste trabalho é o estudo de representações que preservam tipo rho:Gamma - PU(2,1) de grupos triangulares Gamma no grupo de isometrias holomorfas do espaço hiperbólico complexo de dimensão dois H2C. O grupo triangular Gamma(p,q,r) é o grupo gerado por reflexões nos lados de um triângulo geodésico, com ângulos pi/p, pi/q e pi/r, no plano hiperbólico. Neste trabalho, nossas atenções são voltadas para os grupos Gamma (4,4,infinito) e Gamma(4,infinito,infinito). Demonstramos, entre outros resultados: Par

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32

Fayers, Matthew. "Representations of symmetric groups and Schur algebras." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620642.

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33

Mazhar, Siddiqua. "Composition of permutation representations of triangle groups." Thesis, University of Newcastle upon Tyne, 2017. http://hdl.handle.net/10443/3857.

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A triangle group is denoted by (p, q, r) and has finite presentation (p, q, r) = hx, y|xp = yq = (xy)r = 1i. In the 1960’s Higman conjectured that almost every triangle group has among its homomorphic images all but finitely many of the alternating groups. This was proved by Everitt in [6]. In this thesis, we combine permutation representations using the methods used in the proof of Higman’s conjecture. We do some experiments by using GAP code and then we examine the situations where the composition of a number of coset diagrams for a triangle group is imprimitive. Chapter 1 provides the intro

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34

Kasouha, Abeir Mikhail. "Symmetric representations of elements of finite groups." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2605.

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This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.

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35

Chan, Ping-Shun. "Invariant representations of GSp(2)." Columbus, Ohio : Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1132765381.

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36

Phillips, Aaron M. "Restricting modular spin representations of symmetric and alternating groups /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3095271.

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Thesis (Ph. D.)--University of Oregon, 2003.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 69-71). Also available for download via the World Wide Web; free to University of Oregon users.

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37

Knezevic, Marica. "Graphs of lattices in representations of finite groups." Thesis, King's College London (University of London), 2017. https://kclpure.kcl.ac.uk/portal/en/theses/graphs-of-lattices-in-representations-of-finite-groups(2f435ed5-4a11-4d45-ae2b-26e3c6264ee8).html.

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This thesis work is motivated by the Langlands program, which relates objects from number theory and representation theory. In particular it is motivated by the compatibility of the local and global cases, especially in the mod p case. Given a finite group G, E a finite extension of Qp with ring of integers OE, uniformizer E, V a finite dimensional E-vector space and : G ! AutE(V ) an absolutely irreducible representation, we associate to the following directed graph: its vertices are homothety classes of lattices in V and there is an edge from (the class of) to 0 when E 0 and the quotient =0

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38

Brau, Julio. "Selmer groups of elliptic curves and Galois representations." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708896.

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39

Balagović, Martina. "On representations of quantum groups and Cherednik algebras." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/68478.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 245-248).<br>In the first part of the thesis, we study quantum groups associated to a semisimple Lie algebra g. The classical Chevalley theorem states that for [ a Cartan subalgebra and W the Weyl group of g, the restriction of g-invariant polynomials on g to [ is an isomorphism onto the W-invariant polynomials on , Res: C[g]1 -+ C[]w. A recent generalization of [36] to the case when the target space C of the polynomial maps is

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40

Roth, Calvin L. (Calvin Lee). "Example of solvable quantum groups and their representations." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28104.

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41

Wassink, Luke Samuel. "Split covers for certain representations of classical groups." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1929.

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Let R(G) denote the category of smooth representations of a p-adic group. Bernstein has constructed an indexing set B(G) such that R(G) decomposes into a direct sum over s ∈ B(G) of full subcategories Rs(G) known as Bernstein subcategories. Bushnell and Kutzko have developed a method to study the representations contained in a given subcategory. One attempts to associate to that subcategory a smooth irreducible representation (τ,W) of a compact open subgroup J < G. If the functor V ↦ HomJ(W,V) is an equivalence of categories from Rs(G) → H(G,τ)mod we call (J,τ) a type. Given a Levi subgroup L

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42

Fitzpatrick, Michael Colin. "Continuous families of representations of mapping class groups." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1316.

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The study of mapping class groups began in the 1920s with Max Dehn and Jakob Nielsen. It was about this time that topology was just being developed, so mapping class groups were of immediate interest, being invariants of topological spaces. The works of Dehn and Nielsen were continued by William Harvey in the 1960s and 70s leading to the development of the curve complex, an important construction still very relevant to mathematics today. William Thurston is another important name in this area since he was able to completely classify homeomorphisms of surfaces in 1976, leading to the famous "Ni

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43

Torres, Bisquertt María de la Luz. "Symmetric generation of finite groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2625.

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Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.

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44

Ruff, Oliver. "Completely splittable representations of symmetric groups and affine Hecke algebras /." view abstract or download file of text, 2005. http://wwwlib.umi.com/cr/uoregon/fullcit?p3190545.

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Thesis (Ph. D.)--University of Oregon, 2005.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 44-45). Also available for download via the World Wide Web; free to University of Oregon users.

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45

Leslie, Spencer. "Theta liftings on higher covers of symplectic groups." Thesis, Boston College, 2018. http://hdl.handle.net/2345/bc-ir:107937.

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Thesis advisor: Solomon Friedberg<br>We study a new lifting of automorphic representations using the theta representation ϴ on the 4-fold cover of the symplectic group, $\overline{\Sp}_{2r}(\A)$. This lifting produces the first examples of CAP representations on higher degree metaplectic covering groups. Central to our analysis is the identification of the maximal nilpotent orbit associated to ϴ. We conjecture a natural extension of Arthur's parameterization of the discrete spectrum to $\overline{\Sp}_{2r}(\A)$. Assuming this, we compute the effect of our lift on Arthur parameters and show tha

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46

May, Jessica. "Matrix Representation of Knot and Link Groups." Scholarship @ Claremont, 2006. https://scholarship.claremont.edu/hmc_theses/185.

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In the 1960s French mathematician George de Rham found a relationship between two invariants of knots. He found that there exist representations of the fundamental group of a knot into a group G of upper right triangular matrices in C with determinant one that is described exactly by the roots of the Alexander polynomial. I extended this result to find that the representations of the fundamental group of a link into G are described by the multivariable Alexander polynomial of the link.

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47

Knight, Jason. "Various methods for calculating reducible and irreducible representations of the symmetric group a thesis presented to the faculty of the Graduate School, Tennessee Technological University /." Click to access online, 2009. http://proquest.umi.com/pqdweb?index=30&sid=1&srchmode=1&vinst=PROD&fmt=6&startpage=-1&clientid=28564&vname=PQD&RQT=309&did=1760001861&scaling=FULL&ts=1251310430&vtype=PQD&rqt=309&TS=1251310467&clientId=28564.

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48

Housley, Matthew. "Polynomial representations and associated cycles for indefinite unitary groups." THE UNIVERSITY OF UTAH, 2012. http://pqdtopen.proquest.com/#viewpdf?dispub=3461625.

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49

Lemieux, Stephane R. "Minimal degree of faithful permutation representations of finite groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0015/MQ48492.pdf.

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50

Sin, P. K. W. "Some problems on induced modular representations of finite groups." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375304.

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