0000000000433682

AUTHOR

D. Lebedev

showing 2 related works from this author

Unitary Representations of the Modular and Two-Particle Q-Deformed Toda Chains

2001

The paper deals with the analytic theory of the quantum two-particle q-deformed Toda chains. This is the simplest nontrivial example clarifying 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 and Whittaker functions are presented in terms of the double sine functions.

Pure mathematicsUnitary representationExplicit formulaeReal formDuality (optimization)Mathematics::Representation TheoryHopf algebraWhittaker functionUnitary stateRepresentation theoryMathematics
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Unitary Representations of U q (𝔰𝔩}(2,ℝ)),¶the Modular Double and the Multiparticle q -Deformed¶Toda Chain

2002

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.

Pure mathematicsUnitary representationChain (algebraic topology)Quantum groupLie groupDuality (optimization)Statistical and Nonlinear PhysicsFunctional equation (L-function)Quantum inverse scattering methodRepresentation theoryMathematical PhysicsMathematicsCommunications in Mathematical Physics
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