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Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians

M. Noumi·M. S. Dijkhuizen·T. Sugitani
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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.

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BibTeXRIS

M. Noumi, M. S. Dijkhuizen, T. Sugitani. 1996-03-15. Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians. https://arxiv.org/abs/q-alg/9603014

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