Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials

E. Buffenoir (1, 2) , Ph. Roche (1, 2)

1 LPTA - Laboratoire de Physique Théorique et Astroparticules
2 PMT - Laboratoire de Physique Mathématique et Théorique

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.

Mots clés: quantum theory; group theory; polynomials; angular momentum theory; tensors. KeyWords Plus: 2D GRAVITY

Domaines: Algèbres quantiques [math.QA]; Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

E. Buffenoir, Ph. Roche. Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials. Journal of Mathematical Physics, 2000, 41, pp.7715-7751. ⟨10.1063/1.1289828⟩. ⟨hal-00178188⟩