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2 results

  • 6 - Elliptic Hypergeometric Functions Associated with Root Systems

  • Edited by Tom H. Koornwinder, Universiteit van Amsterdam, Jasper V. Stokman, Universiteit van Amsterdam
  • Book:
    Encyclopedia of Special Functions: The Askey-Bateman Project
    Published online:
    30 September 2020
    Print publication:
    15 October 2020, pp 159-186

  • Summary

    We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two in essence form an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integrals and series on root systems. The third and final part gives an introduction to Rains' elliptic Macdonald-Koornwinder theory (in part also developed by Coskun and Gustafson). We survey the main properties of elliptic BC_n interpolation functions and BC_n-symmetric biorthogonal functions, which generalize Okounkov's BC_n interpolation Macdonald polynomials and the Koornwinder polynomials, respectively.

  • Elliptic determinant evaluations and the Macdonald identities for affine root systems

  • Hjalmar Rosengren, Michael Schlosser
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 4 / July 2006
    Published online by Cambridge University Press:
    14 July 2006, pp. 937-961
    Print publication:
    July 2006
    • Article
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  • We obtain several determinant evaluations, related to affine root systems, which provide elliptic extensions of Weyl denominator formulas. Some of these are new, also in the polynomial special case, while others yield new proofs of the Macdonald identities for the seven infinite families of irreducible reduced affine root systems.