Unitary Representations of Quantum Lorentz Group and Quantum Relativistic Toda Chain

Details Unitary Representations of Quantum Lorentz Group and Quantum Relativistic Toda Chain Unitary Representations of Quantum Lorentz Group and Quantum Relativistic Toda Chain

2001-10-17

arxiv.org/abs/math/0110182v1

Mathematics

Quantum Algebra

Latex, 25 pages

Scientific paper

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.

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