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Isomorphism classes of A-hypergeometric systems

Mutsumi Saito
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Abstract

For a finite set A of integral vectors, Gel'fand, Kapranov and Zelevinskii defined a system of differential equations with a parameter vector as a D-module, which system is called an A-hypergeometric (or a GKZ hypergeometric) system. Classifying the parameters according to the D-isomorphism classes of their corresponding A-hypergeometric systems is one of the most fundamental problems in the theory. In this paper we give a combinatorial answer for the problem under the assumption that the finite set A lies in a hyperplane off the origin, and illustrate it in two particularly simple cases: the normal case and the monomial curve case.

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Mutsumi Saito. 1999-12-28. Isomorphism classes of A-hypergeometric systems. https://arxiv.org/abs/math/9912213

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