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Elliptic U(2) Quantum Group and Elliptic Hypergeometric Series

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Abstract

We investigate an elliptic quantum group introduced by Felder and Varchenko, which is constructed from the R-matrix of the Andrews–Baxter–Forrester model, containing both spectral and dynamical parameter. We explicitly compute the matrix elements of certain corepresentations and obtain orthogonality relations for these elements. Using dynamical representations these orthogonality relations give discrete bi-orthogonality relations for terminating very-well-poised balanced elliptic hypergeometric series, previously obtained by Frenkel and Turaev and by Spiridonov and Zhedanov in different contexts.

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Authors and Affiliations

  1. Technische Universiteit Delft, Faculteit Elektrotechniek, Wiskunde en Informatica Toegepaste Wiskundige Analyse, Postbus, 5031, 2600, GA Delft, Netherlands

    Erik Koelink & Yvette van Norden

  2. Department of Mathematics, Chalmers University of Technology and Göteborg University, 412 96, Göteborg, Sweden

    Hjalmar Rosengren

Authors
  1. Yvette van Norden
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  2. Hjalmar Rosengren
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Correspondence to Erik Koelink.

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Communicated by L. Takhtajan

The second author is supported by Netherlands Organisation for Scientific Research (NWO) under project number 613.006.572.

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Koelink, E., Norden, Y. & Rosengren, H. Elliptic U(2) Quantum Group and Elliptic Hypergeometric Series. Commun. Math. Phys. 245, 519–537 (2004). https://doi.org/10.1007/s00220-003-1016-0

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  • DOI: https://doi.org/10.1007/s00220-003-1016-0

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