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.
- Publication:
-
eprint arXiv:q-alg/9603014
- Pub Date:
- March 1996
- DOI:
- 10.48550/arXiv.q-alg/9603014
- arXiv:
- arXiv:q-alg/9603014
- Bibcode:
- 1996q.alg.....3014N
- Keywords:
-
- Mathematics - Quantum Algebra
- E-Print:
- 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