Tensor product of principal unitary representations of quantum Lorentz group and Askey–Wilson polynomials

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 Uq(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.