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Journal of Mathematical Physics 41 (2000) 7715-7751
Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials
E. Buffenoir1, 2, Ph. Roche1, 2

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.
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
2 :  PMT - Laboratoire de Physique Mathématique et Théorique
Mathématiques/Algèbres quantiques

Physique/Relativité Générale et Cosmologie Quantique

Physique/Physique des Hautes Energies - Théorie
quantum theory – group theory – polynomials – angular momentum theory – tensors. KeyWords Plus: 2D GRAVITY
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