Unitary Representations of Quantum Lorentz Group and Quantum Relativistic Toda Chain
Abstract
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.
Keywords
Cite
@article{arxiv.math/0110182,
title = {Unitary Representations of Quantum Lorentz Group and Quantum Relativistic Toda Chain},
author = {M. A. Olshanetsky and V. -B. K. Rogov},
journal= {arXiv preprint arXiv:math/0110182},
year = {2007}
}
Comments
Latex, 25 pages