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arxiv: math/0501405 · v2 · submitted 2005-01-24 · 🧮 math.QA · math.RT

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

Fokko J. van de Bult
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classification 🧮 math.QA math.RT
keywords doubleeigenfunctionsfunctionhypergeometricmodularruijsenaarsalgebraaskey-wilson
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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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