Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians

Abstract

We present a one-parameter family of constant solutions of the reflection equation and define a family of quantum complex Grassmannians endowed with a transitive action of the quantum unitary group. By computing the radial part of a suitable Casimir operator, we identify the zonal spherical functions (i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional irreducible representations) as multivariable Askey-Wilson polynomials containing two continuous and two discrete parameters.

11 pages, AMS-TeX 2.1, no figures. To appear in: Proceedings of a Workshop on Special Functions, q-Series and Related Topics, Toronto, June 19-23, 1995, Fields Inst. Comm