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1997 | OriginalPaper | Buchkapitel

Combinatorics of hypergeometric functions associated with positive roots

verfasst von : Israel M. Gelfand, Mark I. Graev, Alexander Postnikov

Erschienen in: The Arnold-Gelfand Mathematical Seminars

Verlag: Birkhäuser Boston

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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.

Metadaten
Titel
Combinatorics of hypergeometric functions associated with positive roots
verfasst von
Israel M. Gelfand
Mark I. Graev
Alexander Postnikov
Copyright-Jahr
1997
Verlag
Birkhäuser Boston
DOI
https://doi.org/10.1007/978-1-4612-4122-5_10