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

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

2001-02-26

arxiv.org/abs/hep-th/0102180v2

Commun.Math.Phys. 225 (2002) 573-609

Physics

High Energy Physics

High Energy Physics - Theory

AmsLatex, 41 pages, 3 figures

Scientific paper

10.1007/s002200100592

The paper deals with the analytic theory of the quantum q-deformed Toda chain; the technique used combines the methods of representation theory and the Quantum Inverse Scattering Method. The key phenomenon which is under scrutiny is the role of the modular duality concept (first discovered by L.Faddeev) in the representation theory of noncompact semisimple quantum groups. Explicit formulae for the Whittaker vectors are presented in terms of the double sine functions and the wave functions of the N-particle q-deformed open Toda chain are given as a multiple integral of the Mellin-Barnes type. For the periodic chain the two dual Baxter equations are derived.

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