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 Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 1, Pages 235–280 (Mi izv8211)

Maximally reducible monodromy of bivariate hypergeometric systems

a Siberian Federal University, Krasnoyarsk
b Plekhanov Russian State University of Economics, Moscow
c Department of Mathematics, Galatasaray University, Istanbul, Turkey

Abstract: We investigate the branching of solutions of holonomic bivariate Horn-type hypergeometric systems. Special attention is paid to invariant subspaces of Puiseux polynomial solutions. We mainly study Horn systems defined by simplicial configurations and Horn systems whose Ore–Sato polygons are either zonotopes or Minkowski sums of a triangle and segments proportional to its sides. We prove a necessary and sufficient condition for the monodromy representation to be maximally reducible, that is, for the space of holomorphic solutions to split into a direct sum of one-dimensional invariant subspaces.

Keywords: hypergeometric system of equations, monodromy representation, monodromy reducibility, intertwining operator.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-31-20008 ìîë_à_âåä13-01-12417-îôè-ì2 Japan Society for the Promotion of Science 20540086 Siberian Branch of Russian Academy of Sciences 14.Y26.31.0006 The first author was supported by a grant from the Government of the Russian Federation for investigations under the guidance of the leading scientists of the Siberian Federal University (contract no. 14.Y26.31.0006), by grants from the Russian Foundation for Basic Research (nos. 13-01-12417-ofi-m2, 15-31-20008-mol-a-ved), as well as by the Japanese Society for the Promotion of Science. The second author was supported by JSPS grant no. 20540086.

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DOI: https://doi.org/10.4213/im8211

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English version:
Izvestiya: Mathematics, 2016, 80:1, 221–262

Bibliographic databases:

UDC: 517.55+517.956
MSC: 33C70, 14M25, 32C38, 32D15, 32S40, 35N10, 57M05

Citation: T. M. Sadykov, S. Tanabé, “Maximally reducible monodromy of bivariate hypergeometric systems”, Izv. RAN. Ser. Mat., 80:1 (2016), 235–280; Izv. Math., 80:1 (2016), 221–262

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. T. M. Sadykov, “On the Analytic Complexity of Hypergeometric Functions”, Proc. Steklov Inst. Math., 298 (2017), 248–255
2. M. Yu. Kalmykov, B. A. Kniehl, “Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation”, J. High Energy Phys., 2017, no. 7, 031, 27 pp.
3. S. Tanabé, “On monodromy representation of period integrals associated to an algebraic curve with bi-degree $(2,2)$”, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat., 25:1 (2017), 207–231
4. T. M. Sadykov, “Computational problems of multivariate hypergeometric theory”, Program. Comput. Softw., 44:2 (2018), 131–137
5. S. I. Bezrodnykh, “The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications”, Russian Math. Surveys, 73:6 (2018), 941–1031
6. Berkesch Ch., Matusevich L.F., Walther U., “Torus Equivariant D-Modules and Hypergeometric Systems”, Adv. Math., 350 (2019), 1226–1266
7. Fernandez-Fernandez M.-C., “On the Local Monodromy of a-Hypergeometric Functions and Some Monodromy Invariant Subspaces”, Rev. Mat. Iberoam., 35:3 (2019), 949–961
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