Askey-wilson functions and quantum groups

Abstract

Eigenfunctions of the Askey-Wilson second order q-difference operator for 0 < q < 1 and lql = 1 are constructed as formal matrix coefficients of the principal series representation of the quantized universal enveloping algebra Uq(s1(2C,)).T he eigenfunctions are given in integral form. We show that for 0 < q < 1 the resulting eigenfunction can be rewritten as a very-well-poised 8p7-series, and reduces for special parameter values to a natural elliptic analogue of the cosine kernel. © 2005 Springer Science+Business Media, Inc.