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Journal articles on the topic 'Monodromy representations'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

IMAYOSHI, YOICHI, MANABU ITO, and HIROSHI YAMAMOTO. "A REDUCIBILITY PROBLEM FOR MONODROMY OF SOME SURFACE BUNDLES." Journal of Knot Theory and Its Ramifications 13, no. 05 (2004): 597–616. http://dx.doi.org/10.1142/s0218216504003330.

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A surface bundle determines a monodromy representation recording the twisting of the fiber under transport around a closed path in the base space. The fascinating relation between these monodromy representations and the Thurston classification of surface automorphisms will be studied. In this note we deal with a simple and interesting case: the fibrations of Fadell and Neuwirth.

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2

Kamada, Seiichi. "Graphic descriptions of monodromy representations." Topology and its Applications 154, no. 7 (2007): 1430–46. http://dx.doi.org/10.1016/j.topol.2006.04.024.

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3

Aaltonen, Martina. "Monodromy representations of completed coverings." Revista Matemática Iberoamericana 32, no. 2 (2016): 533–70. http://dx.doi.org/10.4171/rmi/894.

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4

FELDER, G., V. TARASOV, and A. VARCHENKO. "MONODROMY OF SOLUTIONS OF THE ELLIPTIC QUANTUM KNIZHNIK–ZAMOLODCHIKOV–BERNARD DIFFERENCE EQUATIONS." International Journal of Mathematics 10, no. 08 (1999): 943–75. http://dx.doi.org/10.1142/s0129167x99000410.

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The elliptic quantum Knizhnik–Zamolodchikov–Bernard (qKZB) difference equations associated to the elliptic quantum group Eτ,η(sl2) is a system of difference equations with values in a tensor product of representations of the quantum group and defined in terms of the elliptic R-matrices associated with pairs of representations of the quantum group. In this paper we solve the qKZB equations in terms of elliptic hypergeometric functions and describe the monodromy properties of solutions. It turns out that the monodromy transformations of solutions are described in terms of elliptic R-matrices ass

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5

LAWRENCE, R. J. "A TOPOLOGICAL APPROACH TO REPRESENTATIONS OF THE IWAHORI-HECKE ALGEBRA." International Journal of Modern Physics A 05, no. 16 (1990): 3213–19. http://dx.doi.org/10.1142/s0217751x90002178.

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In this paper a topological construction of representations of the [Formula: see text]-series of Hecke algebras, associated with 2-row Young diagrams, will be announced. This construction gives the representations in terms of the monodromy representation obtained from a vector bundle over the configuration space of η points in the complex plane. The fibres are homology spaces of configuration spaces of points in a punctured complex plane, with a suitable twisted local coefficient system, and there is thus a natural flat connection on the vector bundle. It is also shown that there is a close co

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6

Todorov, I. T., and L. K. Hadjiivanov. "Monodromy representations of the braid group." Physics of Atomic Nuclei 64, no. 12 (2001): 2059–68. http://dx.doi.org/10.1134/1.1432899.

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7

Gupta, Subhojoy, and Mahan Mj. "Monodromy representations of meromorphic projective structures." Proceedings of the American Mathematical Society 148, no. 5 (2020): 2069–78. http://dx.doi.org/10.1090/proc/14866.

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8

Simha, R. R. "The monodromy representations of projective structures." Archiv der Mathematik 52, no. 4 (1989): 413–16. http://dx.doi.org/10.1007/bf01194420.

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9

Tanabé, Susumu. "On monodromy representation of period integrals associated to an algebraic curve with bi-degree (2,2)." Analele Universitatii "Ovidius" Constanta - Seria Matematica 25, no. 1 (2017): 207–31. http://dx.doi.org/10.1515/auom-2017-0016.

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AbstractWe study a problem related to Kontsevich's homological mirror symmetry conjecture for the case of a generic curve Y with bi-degree (2,2) in a product of projective lines ℙ1× ℙ1. We calculate two differenent monodromy representations of period integrals for the affine variety X(2,2)obtained by the dual polyhedron mirror variety construction from Y. The first method that gives a full representation of the fundamental group of the complement to singular loci relies on the generalised Picard-Lefschetz theorem. The second method uses the analytic continuation of the Mellin-Barnes integrals

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10

Berman, Leah Wrenn, Barry Monson, Déborah Oliveros, and Gordon I. Williams. "Fully truncated simplices and their monodromy groups." Advances in Geometry 18, no. 2 (2018): 193–206. http://dx.doi.org/10.1515/advgeom-2017-0047.

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Abstract We describe a simple way to manufacture faithful representations of the monodromy group of an n-polytope. This is used to determine the monodromy group for 𝓣n, the fully truncated n-simplex. As by-products, we get the minimal regular cover for 𝓣n, along with the analogous objects for a prism over a simplex.

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11

Boyer, Pascal. "Conjecture de monodromie-poids pour quelques variétés de Shimura unitaires." Compositio Mathematica 146, no. 2 (2010): 367–403. http://dx.doi.org/10.1112/s0010437x09004588.

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AbstractIn Boyer [Monodromy of perverse sheaves on vanishing cycles on some Shimura varieties, Invent. Math. 177 (2009), 239–280 (in French)], a sheaf version of the monodromy-weight conjecture for some unitary Shimura varieties was proved by giving explicitly the monodromy filtration of the complex of vanishing cycles in terms of local systems introduced in Harris and Taylor [The geometry and cohomology of some simple Shimura varieties (Princeton University Press, Princeton, NJ, 2001)]. The main result of this paper is the cohomological version of the monodromy-weight conjecture for these Shi

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12

Carlson, James A., and Domingo Toledo. "Discriminant complements and kernels of monodromy representations." Duke Mathematical Journal 97, no. 3 (1999): 621–48. http://dx.doi.org/10.1215/s0012-7094-99-09723-5.

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13

Patrikis, Stefan. "Deformations of Galois representations and exceptional monodromy." Inventiones mathematicae 205, no. 2 (2015): 269–336. http://dx.doi.org/10.1007/s00222-015-0635-3.

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14

Stafa, Mentor. "On monodromy representations in Denham–Suciu fibrations." Journal of Pure and Applied Algebra 219, no. 8 (2015): 3372–90. http://dx.doi.org/10.1016/j.jpaa.2014.12.001.

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15

Stafa, Mentor. "Polyhedral products, flag complexes and monodromy representations." Topology and its Applications 244 (August 2018): 12–30. http://dx.doi.org/10.1016/j.topol.2018.06.001.

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16

Leibman, A. "Some monodromy representations of generalized braid groups." Communications in Mathematical Physics 164, no. 2 (1994): 293–304. http://dx.doi.org/10.1007/bf02101704.

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17

Goto, Yoshiaki, and Keiji Matsumoto. "The monodromy representation and twisted period relations for Appell’s hypergeometric function F 4." Nagoya Mathematical Journal 217 (March 2015): 61–94. http://dx.doi.org/10.1017/s0027763000026957.

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AbstractWe consider the systemF4(a, b, c)of differential equations annihilating Appell's hypergeometric seriesF4(a,b,c;x). We find the integral representations for four linearly independent solutions expressed by the hypergeometric seriesF4. By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation ofF4(a, b, c)and the twisted period relations for the fundamental systems of solutions ofF4.

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18

Adachi, Shunya. "Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities." Opuscula Mathematica 42, no. 3 (2022): 361–91. http://dx.doi.org/10.7494/opmath.2022.42.3.361.

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We study the monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities. The moduli space of our monodromy representations can be realized by certain affine cubic surface. In this paper we characterize the irreducible monodromies having the non-degenerate invariant Hermitian forms in terms of that cubic surface. The explicit forms of invariant Hermitian forms are also given. Our result may bring a new insight into the study of the Painlev� differential equations.

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19

Ikeda, Akishi. "Homological and Monodromy Representations of Framed Braid Groups." Communications in Mathematical Physics 359, no. 3 (2017): 1091–121. http://dx.doi.org/10.1007/s00220-017-3036-1.

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20

Polizzi, Francesco. "Monodromy representations and surfaces with maximal Albanese dimension." Bollettino dell'Unione Matematica Italiana 11, no. 1 (2017): 107–19. http://dx.doi.org/10.1007/s40574-017-0131-3.

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21

Mornev, M. "Local monodromy of Drinfeld modules." Compositio Mathematica 160, no. 11 (2024): 2656–83. https://doi.org/10.1112/s0010437x24007450.

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Compared with algebraic varieties the local monodromy of Drinfeld modules appears to be hopelessly complex: the image of the wild inertia subgroup under Tate module representations is infinite save for the case of potential good reduction. Nonetheless, we show that Tate modules of Drinfeld modules are ramified in a limited way: the image of a sufficiently deep ramification subgroup is trivial. This leads to a new invariant, the local conductor of a Drinfeld module. We establish an upper bound on the conductor in terms of the volume of the period lattice. As an intermediate step we develop a th

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22

Shimizu, Koji. "A -adic monodromy theorem for de Rham local systems." Compositio Mathematica 158, no. 12 (2022): 2157–205. http://dx.doi.org/10.1112/s0010437x2200776x.

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We study horizontal semistable and horizontal de Rham representations of the absolute Galois group of a certain smooth affinoid over a $p$ -adic field. In particular, we prove that a horizontal de Rham representation becomes horizontal semistable after a finite extension of the base field. As an application, we show that every de Rham local system on a smooth rigid analytic variety becomes horizontal semistable étale locally around every classical point. We also discuss potentially crystalline loci of de Rham local systems and cohomologically potentially good reduction loci of smooth proper mo

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23

Goto, Yoshiaki, and Keiji Matsumoto. "The monodromy representation and twisted period relations for Appell’s hypergeometric function F4." Nagoya Mathematical Journal 217 (March 2015): 61–94. http://dx.doi.org/10.1215/00277630-2873714.

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AbstractWe consider the system F4 (a, b, c) of differential equations annihilating Appell's hypergeometric series F4(a,b,c;x). We find the integral representations for four linearly independent solutions expressed by the hypergeometric series F4. By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation of F4(a, b, c) and the twisted period relations for the fundamental systems of solutions of F4.

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24

LEE, H. C., M. L. GE, M. COUTURE, and Y. S. WU. "STRANGE STATISTICS, BRAID GROUP REPRESENTATIONS AND MULTIPOINT FUNCTIONS IN THE N-COMPONENT MODEL." International Journal of Modern Physics A 04, no. 09 (1989): 2333–70. http://dx.doi.org/10.1142/s0217751x89000947.

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The statistics of fields in low dimensions is studied from the point of view of the braid group Bn of n strings. Explicit representations MR for the N-component model, N=2 to 5, are derived by solving the Yang-Baxter-like braid group relations for the statistical matrix R, which describes the transformation of the bilinear product of two N-component fields under the transposition of coordinates. When R2≠1 the statistics is neither Bose-Einstein nor Fermi-Dirac; it is strange. It is shown that for each N, the N+1 parameter family of solutions obtained is the most general one under a given set o

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25

PONSOT, B. "MONODROMY OF SOLUTIONS OF THE KNIZHNIK-ZAMOLODCHIKOV EQUATION: SL(2)k WZNW MODEL." International Journal of Modern Physics A 19, supp02 (2004): 336–47. http://dx.doi.org/10.1142/s0217751x04020506.

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Three explicit and equivalent representations for the monodromy of the conformal blocks in the non compact SL(2)k WZNW model are proposed in terms of the same quantity computed in Liouville field theory.

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26

Saito, Takeshi. "Hilbert modular forms and p-adic Hodge theory." Compositio Mathematica 145, no. 5 (2009): 1081–113. http://dx.doi.org/10.1112/s0010437x09004175.

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AbstractFor the p-adic Galois representation associated to a Hilbert modular form, Carayol has shown that, under a certain assumption, its restriction to the local Galois group at a finite place not dividing p is compatible with the local Langlands correspondence. Under the same assumption, we show that the same is true for the places dividing p, in the sense of p-adic Hodge theory, as is shown for an elliptic modular form. We also prove that the monodromy-weight conjecture holds for such representations.

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27

YAU, MEI-LIN. "CYLINDRICAL CONTACT HOMOLOGY OF A DEHN TWIST." International Journal of Mathematics 20, no. 12 (2009): 1479–525. http://dx.doi.org/10.1142/s0129167x09005819.

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We use open book representations of contact 3-manifolds to compute the cylindrical contact homology of a Stein-fillable contact 3-manifold represented by the open book whose monodromy is a positive Dehn twist on a torus with boundary.

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28

Dunkl, Charles. "Differential-difference operators and monodromy representations of Hecke algebras." Pacific Journal of Mathematics 159, no. 2 (1993): 271–98. http://dx.doi.org/10.2140/pjm.1993.159.271.

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29

Millson, John J., and Valerio Toledano Laredo. "Casimir Operators and Monodromy Representations of Generalised Braid Groups." Transformation Groups 10, no. 2 (2005): 217–54. http://dx.doi.org/10.1007/s00031-005-1008-6.

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30

Kohno, Toshitake. "Monodromy representations of braid groups and Yang-Baxter equations." Annales de l’institut Fourier 37, no. 4 (1987): 139–60. http://dx.doi.org/10.5802/aif.1114.

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31

Hui, Chun Yin. "Monodromy of Galois representations and equal-rank subalgebra equivalence." Mathematical Research Letters 20, no. 4 (2013): 705–25. http://dx.doi.org/10.4310/mrl.2013.v20.n4.a8.

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32

Chen, Zhijie, Ting-Jung Kuo, Chang-Shou Lin, and Kouichi Takemura. "On reducible monodromy representations of some generalized Lamé equation." Mathematische Zeitschrift 288, no. 3-4 (2017): 679–88. http://dx.doi.org/10.1007/s00209-017-1906-z.

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33

Corlette, Kevin, and Carlos Simpson. "On the classification of rank-two representations of quasiprojective fundamental groups." Compositio Mathematica 144, no. 5 (2008): 1271–331. http://dx.doi.org/10.1112/s0010437x08003618.

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AbstractSuppose that X is a smooth quasiprojective variety over ℂ and ρ:π1(X,x)→SL(2,ℂ) is a Zariski-dense representation with quasiunipotent monodromy at infinity. Then ρ factors through a map X→Y with Y either a Deligne–Mumford (DM) curve or a Shimura modular stack.

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34

Haraoka, Yoshishige, and Toshiya Matsumura. "Three-dimensional representations of braid groups associated with some finite complex reflection groups." International Journal of Mathematics 28, no. 14 (2017): 1750109. http://dx.doi.org/10.1142/s0129167x17501099.

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We study the rigidity of three-dimensional representations of braid groups associated with finite primitive irreducible complex reflection groups in [Formula: see text]. In many cases, we show the rigidity. For rigid representations, we give explicit forms of the representations, which turns out to be the monodromy representations of uniformization equations of Saito–Kato–Sekiguchi [Uniformization systems of equations with singularities along the discriminant sets of complex reflection groups of rank three, Kyushu J. Math. 68 (2014) 181–221; On the uniformization of complements of discriminant

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35

LAWRENCE, RUTH J. "BRAID GROUP REPRESENTATIONS ASSOCIATED WITH ${\mathfrak{sl}}_m$." Journal of Knot Theory and Its Ramifications 05, no. 05 (1996): 637–60. http://dx.doi.org/10.1142/s0218216596000370.

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It has been seen elsewhere how elementary topology may be used to construct representations of the Iwahori-Hecke algebra associated with two-row Young diagrams, and how these constructions are related to the production of the same representations from the monodromy of n-point correlation functions in the work of Tsuchiya & Kanie and to the construction of the one-variable Jones polynomial. This paper investigates the extension of these results to representations associated with arbitrary multi-row Young diagrams and a functorial description of the two-variable Jones polynomial of links in

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36

Yang, YanHong. "The Fixed Point Locus of the Verschiebung on ℳX(2, 0) for Genus-2 Curves X in Charateristic 2". Canadian Mathematical Bulletin 57, № 2 (2014): 439–48. http://dx.doi.org/10.4153/cmb-2013-019-1.

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Abstract.We prove that for every ordinary genus-2 curve X over a finite field κ of characteristic 2 with Aut(X/κ) = ℤ/2ℤ × S3 there exist SL(2; κ[[s]])-representations of π1(X) such that the image of π1(X̄) is infinite. This result produces a family of examples similar to Y. Laszlo’s counterexample to A. J. de Jong’s question regarding the finiteness of the geometric monodromy of representations of the fundamental group.

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37

ARNAUDON, D., A. DOIKOU, L. FRAPPAT, É. RAGOUCY, and N. CRAMPÉ. "ANALYTICAL BETHE ANSATZ FOR OPEN SPIN CHAINS WITH SOLITON NONPRESERVING BOUNDARY CONDITIONS." International Journal of Modern Physics A 21, no. 07 (2006): 1537–54. http://dx.doi.org/10.1142/s0217751x06029077.

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We present an "algebraic treatment" of the analytical Bethe ansatz for open spin chains with soliton nonpreserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe ansatz. It allows us to deal with a generic [Formula: see text] open SNP spin chain possessing on each site an arbitrary representation. As a result, we obtain the Bethe equations in their full generality. The classification of finite dimensional irreducible representations for the twisted Yangians are directly linked to t

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38

Daskalopoulos, G., S. Dostoglou, and R. Wentworth. "Families of SU(2) representations for mapping cylinders of periodic monodromy." Proceedings of the Edinburgh Mathematical Society 40, no. 2 (1997): 383–92. http://dx.doi.org/10.1017/s0013091500023828.

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We examine the action of diffeomorphisms of an oriented surface with boundary on the space of conjugacy classes of SU(2) representations of the fundamental group and prove that in the case of a single periodic diffeomorphism the induced action always has fixed points. For the corresponding 3-dimensional mapping cylinders we obtain families of representations parametrized by their value on the longitude of the torus boundary.

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39

Hussenot Desenonges, Nicolas. "On the dynamics of Riccati foliations with nonparabolic monodromy representations." Conformal Geometry and Dynamics of the American Mathematical Society 23, no. 10 (2019): 164–88. http://dx.doi.org/10.1090/ecgd/337.

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40

Larsen, M., and R. Pink. "On ? of algebraic monodromy groups in compatible systems of representations." Inventiones Mathematicae 107, no. 1 (1992): 603–36. http://dx.doi.org/10.1007/bf01231904.

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41

Cherednik, Ivan. "Monodromy representations for generalized Knizhnik-Zamolodchikov equations and Hecke algebras." Publications of the Research Institute for Mathematical Sciences 27, no. 5 (1991): 711–26. http://dx.doi.org/10.2977/prims/1195169268.

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42

Allen, Patrick B., and James Newton. "Monodromy for Some Rank Two Galois Representations over CM Fields." Documenta Mathematica 25 (2020): 2487–506. http://dx.doi.org/10.4171/dm/805.

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43

TARASOV, VITALY O. "CYCLIC MONODROMY MATRICES FOR THE R-MATRIX OF THE SIX-VERTEX MODEL AND THE CHIRAL POTTS MODEL WITH FIXED SPIN BOUNDARY CONDITIONS." International Journal of Modern Physics A 07, supp01b (1992): 963–75. http://dx.doi.org/10.1142/s0217751x92004129.

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Irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model are described. As a consequence, the direct computation of spectra for transfer-matrices of the chiral Potts model with special fixed-spin boundary conditions is done. The generalization of simple Baxter's Hamiltonian is proposed.

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44

Tang, Shiang. "Algebraic monodromy groups of l-adic representations of Gal(ℚ∕ℚ)". Algebra & Number Theory 13, № 6 (2019): 1353–94. http://dx.doi.org/10.2140/ant.2019.13.1353.

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45

Matsumoto, Keiji. "Monodromy representations of hypergeometric systems with respect to fundamental series solutions." Tohoku Mathematical Journal 69, no. 4 (2017): 547–70. http://dx.doi.org/10.2748/tmj/1512183629.

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46

Bakker, Benjamin, and Jacob Tsimerman. "p-torsion monodromy representations of elliptic curves over geometric function fields." Annals of Mathematics 184, no. 3 (2016): 709–44. http://dx.doi.org/10.4007/annals.2016.184.3.2.

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47

Haraoka, Yoshishige. "Monodromy Representations of Systems of Differential Equations Free from Accessory Parameters." SIAM Journal on Mathematical Analysis 25, no. 6 (1994): 1595–621. http://dx.doi.org/10.1137/s0036141092242228.

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48

GYOJA, A. "Certain unipotent representations of finite Chevalley groups and Picard–Lefschetz monodromy." Annales Scientifiques de l’École Normale Supérieure 35, no. 3 (2002): 437–44. http://dx.doi.org/10.1016/s0012-9593(02)01096-0.

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49

Nakamura, Hiroaki. "Coupling of universal monodromy representations of Galois-Teichm�ller modular groups." Mathematische Annalen 304, no. 1 (1996): 99–119. http://dx.doi.org/10.1007/bf01446287.

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50

Patrikis, Stefan. "Deformations of Galois representations and exceptional monodromy, II: raising the level." Mathematische Annalen 368, no. 3-4 (2016): 1465–91. http://dx.doi.org/10.1007/s00208-016-1459-1.

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