Zonal Spherical Functions on Quantum Grassmann Manifolds

J. Math. Sci. Univ. Tokyo
Vol. 6 (1999), No. 2, Page 335--369.

Sugitani, Tetsuya
Zonal Spherical Functions on Quantum Grassmann Manifolds
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Abstract:
We give an explicit description of the zonal spherical functions on quantum Grassmann manifolds of orthogonal and symplectic type. A unified parametrization of their zonal spherical functions is given in terms of Macdonald polynomials and Koornwinder's multivariable Askey-Wilson polynomials.

Mathematics Subject Classification (1991): Primary 17B37, 33D80
Mathematical Reviews Number: MR1706952

Received: 1996-02-06