Unitary Representations of Quantum Lorentz Group and Quantum Relativistic Toda Chain

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The aim of this paper is to give a group theoretical interpretation of the three types of Bessel-Jackson functions. We consider a family of quantum Lorentz groups and a family of quantum Lobachevsky spaces. For three members of quantum Lobachevsky spaces the Casimir operators give rise to the two-body relativistic open Toda lattice Hamiltonians. Their eigen-functions are the modified Bessel-Jackson functions of three types. We construct the principal series of unitary irreducible representations of the quantum Lorentz groups. Special matrix elements in the irreducible spaces are the Bessel-Macdonald-Jackson functions. They are the wave functions of the two-body relativistic open Toda lattice. We obtain integral representations for these functions.
Latex, 25 pages

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Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/62417

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0110182
 http://arxiv.org/abs/math/0110182

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arXiv