A Generalized Hypergeometric System

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J. Math. Sci. Univ. Tokyo
Vol. 20 (2013), No. 2, Page 285–315.

Ochiai, Hiroyuki ; Zunderiya, Uuganbayar
A Generalized Hypergeometric System
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
We give a combinatorial formula of the dimension of global solutions to a generalization of Gauss-Aomoto-Gelfand hypergeometric system, where the quadratic differential operators are replaced by higher order operators. We also derive a polynomial estimate of the dimension of global solutions for the case in $3 \times 3$ variables.

Keywords: Generalized hypergeometric system, Global solution, Kostka number.

Mathematics Subject Classification (2010): Primary 33C70, 35G35; Secondary 05A17.

Mathematical Reviews Number: MR3154382

Received: 2012-09-27

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