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Tensor Products 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.