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

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. (C) 2000 American Institute of Physics. [S0022-2488(00)02010-7].