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.
Publié le : 2000-07-05
Classification:
quantum theory,
group theory,
polynomials,
angular momentum theory,
tensors. KeyWords Plus: 2D GRAVITY,
PACS: 03.65.Fd, 02.20.-a,
[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],
[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc],
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
@article{hal-00178188,
author = {Buffenoir, E. and Roche, Ph.},
title = {Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00178188}
}
Buffenoir, E.; Roche, Ph. Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00178188/