1997 | OriginalPaper | Chapter
Combinatorics of hypergeometric functions associated with positive roots
Authors : Israel M. Gelfand, Mark I. Graev, Alexander Postnikov
Published in: The Arnold-Gelfand Mathematical Seminars
Publisher: Birkhäuser Boston
Included in: Professional Book Archive
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In this paper we study the hypergeometric system on unipotent matrices. This system gives a holonomic D-module. We find the number of independent solutions of this system at a generic point. This number is equal to the famous Catalan number. An explicit basis of Γ-series in solution space of this system is constructed in the paper. We also consider restriction of this system to certain strata. We introduce several combinatorial constructions with trees, polyhedra, and triangulations related to this subject.