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

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

References in corpus (2)

• Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains
• Modular Double of Quantum Group

Cited by in corpus (9)

• Properties of generalized univariate hypergeometric functions
• Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems
• A Relativistic Conical Function and its Whittaker Limits
• Finite-dimensional representations of the elliptic modular double
• The Virasoro fusion kernel and Ruijsenaars' hypergeometric function
• Generalized Cherednik-Macdonald identities
• Some Remarks on Very-Well-Poised 8phi7 Series
• The dual quantum group for the quantum group analogue of the normalizer of SU(1,1) in SL(2,C)
• From hyperbolic to complex Euler integrals