Projection operator method for quantum groups
| dc.creator | Tolstoy, V. N. | |
| dc.date | 2001-04-03 | |
| dc.date.accessioned | 2026-07-07T04:40:58Z | |
| dc.date.available | 2026-07-07T04:40:58Z | |
| dc.description | In these lectures we develop the projection operator method for quantum groups. Here the term "quantum groups" means q-deformed universal enveloping algebras of contragredient Lie (super)algebras of finite growth. Contains of the lectures can be divided on two parts. Basis fragments of the first part are: combinatorial structure of root systems, the q-analog of the Cartan-Weyl basis, the extremal projector and the universal R-matrix for any contragredient Lie (super)algebra of finite growth. The explicit expressions for the extremal projectors and the universal R-matrices are ordered products of special q-series depending on noncommutative Cartan-Weyl generators. In second part we consider some applications of the extremal projectors. Here we use the projector operator method to develop the theory of the Clebsch-Gordan coefficients for the quantum algebras U_q(su(2)) and U_q(su(3)). In particular, we give a very compact general formula for the canonical U_q(su(3))\supset U_q(su(2)) Clebsch-Gordan coefficients in terms of the U_q(su(2)) Wigner 3nj-symbols which are connected with the basic hyperheometric series. Then we apply the projection operator method for the construction of the q-analog of the Gelfand-Tsetlin basis for U_q(su(n)). Finally using analogy between the extremal projector p(U_q(sl(2))) of the quantum algebra U_q(sl(2)) and the δ(x)-function we introduce 'adjoint extremal projectors' p^{(n)}(U_q(sl(2)) (n=1,2,...) which are some generalizations of the extremal projector p(U_q(sl(2))), and which are analogies of the derivatives of the δ(x)-function, δ^{(n)}(x). | |
| dc.description | 28 pages, LaTeX; lectures given at the NATO Advanced Study Institute "Special Functions 2000" | |
| dc.identifier | https://arxiv.org/abs/math/0104045 | |
| dc.identifier | http://arxiv.org/abs/math/0104045 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61227 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10, 17B37, 17B65, 17B67, 17B80, 81R50, 33D67, 33D80, 81R12 | |
| dc.title | Projection operator method for quantum groups | |
| dc.type | text |