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Communications in Mathematical Physics

, Volume 225, Issue 3, pp 573–609 | Cite as

Unitary Representations of Uq(??}(2,ℝ)),¶the Modular Double and the Multiparticle q-Deformed¶Toda Chain

  • S. Kharchev
  • D. Lebedev
  • M. Semenov-Tian-Shansky

Abstract:

The paper deals with the analytic theory of the quantum q-deformed Toda chains; 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.

Keywords

Sine Explicit Formula Representation Theory Quantum Group Unitary Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • S. Kharchev
    • 1
  • D. Lebedev
    • 1
  • M. Semenov-Tian-Shansky
    • 2
  1. 1.Institute of Theoretical and Experimental Physics, Moscow 117259, RussiaRU
  2. 2.Université de Bourgogne, 21078 Dijon, FranceUS

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