Noncompact quantum algebra $u_q(2,1)$
| dc.creator | Smirnov, Yu. F. | |
| dc.creator | Kharitonov, Yu. I. | |
| dc.date | 2003-11-17 | |
| dc.date.accessioned | 2026-07-07T05:02:58Z | |
| dc.date.available | 2026-07-07T05:02:58Z | |
| dc.description | The structure positive of unitary irreducible representations of the noncompact $u_q(2,1)$ quantum algebra that are related to a positive discrete series is examined. With the aid of projection operators for the $su_q(2)$ subalgebra, a $q$-analog of the Gel'fand--Graev formulas is derived in the basis corresponding to the reduction $u_q(2,1)\to su_q(2)\times u(1)$. Projection operators for the $su_q(1,1)$ subalgebra are employed to study the same representations for the reduction $u_q(2,1)\to u(1)\times su_q(1,1)$. The matrix elements of the generators of the $u_q(2,1)$ algebra are computed in this new basis. A general analytic expression for an element of the transformation bracket $<U|T>_q$ between the bases associated with above two reductions (the elements of this matrix are referred to as $q$-Weyl coefficients) is obtained for a general case where the deformation parameter $q$ is not equal to a root of unity. It is shown explicitly that, apart from a phase, $q$-Weyl coefficients coincide with the $q$-Racah coefficients for the $su_q(2)$ quantum algebra. | |
| dc.description | 23 pages, LaTeX (kapproc); to be published in Proceedings of International Symposium "Symmetry in Sciences XIII" (Bregenz, Austria, July 2003) | |
| dc.identifier | https://arxiv.org/abs/math/0311283 | |
| dc.identifier | http://arxiv.org/abs/math/0311283 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69226 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10, 17B37, 17B65, 17B67, 17B80, 81R50, 33D67, 33D80, 81R12 | |
| dc.title | Noncompact quantum algebra $u_q(2,1)$ | |
| dc.type | text |