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Combinatorics of hypergeometric functions associated with positive roots

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The Arnold-Gelfand Mathematical Seminars

Abstract

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.

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Author information

Authors and Affiliations

  1. Dept. of Math., Rutgers University, 08903, New Brunswick, NJ, USA

    Israel M. Gelfand

  2. Dept. of Math., Research Inst, for System Studies RAS, 23 Avtozavodskaya St, Moscow, 109280, Russia

    Mark I. Graev

  3. Dept. of Math., MIT, Cambridge, MA, 02139, USA

    Alexander Postnikov

Authors
  1. Israel M. Gelfand
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  2. Mark I. Graev
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  3. Alexander Postnikov
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Editor information

Editors and Affiliations

  1. Ceremade, Université Paris-Dauphine, 75775, Paris Cedex 16, France

    V. I. Arnold

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    I. M. Gelfand

  3. Department of Mathematics, Harvard University, 02139, Cambridge, MA, USA

    V. S. Retakh

  4. Department of Mathematics, Columbia University, 10027, New York, NY, USA

    M. Smirnov

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© 1997 Birkhäuser Boston

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Gelfand, I.M., Graev, M.I., Postnikov, A. (1997). Combinatorics of hypergeometric functions associated with positive roots. In: Arnold, V.I., Gelfand, I.M., Retakh, V.S., Smirnov, M. (eds) The Arnold-Gelfand Mathematical Seminars. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4122-5_10

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  • DOI: https://doi.org/10.1007/978-1-4612-4122-5_10

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8663-9

  • Online ISBN: 978-1-4612-4122-5

  • eBook Packages: Springer Book Archive

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