Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C))
arXiv:math/0501405 · doi:10.1016/j.aim.2005.05.023
Abstract
Simultaneous eigenfunctions of two Askey-Wilson second order difference operators are constructed as formal matrix coefficients of the principal series representation of the modular double of the quantized universal enveloping algebra U_q(sl(2,C)). These eigenfunctions are shown to be equal to Ruijsenaars' hypergeometric function under a proper parameter correspondence.
Replaced to synchronize formula numbers with the published version. 25 pages