This article is cited in 14 papers

Maximally reducible monodromy of bivariate hypergeometric systems

T. M. Sadykov^ab, S. Tanabé<sup>c

a</sup> 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.

UDC: 517.55+517.956

MSC: 33C70, 14M25, 32C38, 32D15, 32S40, 35N10, 57M05

Received: 13.01.2014

DOI: 10.4213/im8211

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

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