Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials
Quantum Algebra
2014-11-18 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Abstract
We study the tensor product of principal unitary representations of the quantum Lorentz group, prove a decomposition theorem and compute the associated intertwiners. We show that these intertwiners can be expressed in terms of complex continuations of 6j symbols of U_q(su(2)). These intertwiners are expressed in terms of q-Racah polynomials and Askey-Wilson polynomials. The orthogonality of these intertwiners imply some relation mixing these two families of polynomials. The simplest of these relations is the orthogonality of Askey-Wilson polynomials.
Keywords
Cite
@article{arxiv.math/9910147,
title = {Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials},
author = {E. Buffenoir and Ph. Roche},
journal= {arXiv preprint arXiv:math/9910147},
year = {2014}
}
Comments
34 pages LaTex file, no figures