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Quantum Groups and q-Orthogonal Polynomials

Towards a realization of Askey-Wilson polynomials on SUq (2)
  • Masatoshi Noumi
Conference paper

Abstract

Many links are already known between quantum groups and q-orthogonal polynomials. In this article, we will give a survey on recent works concerning the realization of q-analogues of the Jacobi polynomials as spherical functions on the quantum group SU (2). We would like to emphasize that quantum groups and q-orthogonal polynomials have some characteristics in common and that the interaction between the two fields of mathematics will be important for both of them. The latter half of this article is a review on the works [K3–5] by T.H.Koornwinder and [NM1–5] by K.Mimachi and the author. This article, written from the viewpoint of [NM1–5], may be compared with Koornwinder’s survey [K4].

Keywords

Orthogonal Polynomial Quantum Group Spherical Function Jacobi Polynomial Hermitian Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Masatoshi Noumi
    • 1
  1. 1.Department of Mathematics, College of Arts and SciencesUniversity of TokyoKomaba, Meguro-Ku, Tokyo 153Japan

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