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Isomorphism Classes of A-Hypergeometric Systems

Published online by Cambridge University Press:  04 December 2007

Mutsumi Saito
Mutsumi Saito
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan. E-mail: saito@math.sci.hokudai.ac.jp
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Abstract

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Given a finite set A of integral vectors and a parameter vector, Gel'fand, Kapranov, and Zelevinskii defined a system of differential equations, 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.

Keywords

A-hypergeometric systemsisomorphism classessymmetry algebra
Type
Research Article
Information
Compositio Mathematica , Volume 128 , Issue 3 , September 2001 , pp. 323 - 338
Copyright
© 2001 Kluwer Academic Publishers