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

By S. Kharchev, D. Lebedev, M. Semenov-Tian-Shansky. 2001

153 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3df68eba54d927f511b3d4bea18fe108e4bd3410

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Citations in the corpus

Short proofs of the elliptic beta integrals (2004, unknown): “1;!3) and the re ection equation G (a;!)”
Essays on the theory of elliptic hypergeometric functions (2008, methodology): “ related to the Barnes gamma function of the second order, are actively used in the modern mathematical physics in the description of quantum integrable models and representations of quantum algebras [19, 20, 21, 22, 23, 24]. Forthe deﬁnition ofelliptic hypergeometricintegralsoneneeds theelliptic ga”
Notes on SUSY gauge theories on three-sphere (2010, methodology): “For more detailed explanation on this function, we refer to [ 19 , 20].”
Quantum Riemann Surfaces in Chern-Simons Theory (2011, background): “onentiated variable z = eZ0. Enlarging a q-commuting algebra of exponential operators by adding their duals in this manner is sometimes referred to as forming its modular double [19] (also cf. { 87 { [85, 86]). It is important to observe that original and dual variables always mutually commute. For ”
The modular properties and the integral representations of the multiple elliptic gamma functions (2003, background): “In particular, the double sine function S2(z|ω1, ω2) have been studied to construct solutions or operators of certain equations of mathematical physics as in [4] or [ 5 ].”
SUSY gauge theories on squashed three-spheres (2011, background): “See [20, 21] for more details on this function.”