Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians

Details Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians

1996-03-15

arxiv.org/abs/q-alg/9603014v1

Mathematics

Quantum Algebra

11 pages, AMS-TeX 2.1, no figures. To appear in: Proceedings of a Workshop on Special Functions, q-Series and Related Topics,

Scientific paper

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.

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