Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C))

Details Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C)) Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C))

2005-01-24

arxiv.org/abs/math/0501405v2

Adv. Math. 204 (2006), 539-571

Mathematics

Quantum Algebra

Replaced to synchronize formula numbers with the published version. 25 pages

Scientific paper

10.1016/j.aim.2005.05.023

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.

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