Classification of irreducible representations of the q-deformed algebra U'_q(so_n)
| dc.creator | Klimyk, A. U. | |
| dc.date | 2001-10-03 | |
| dc.date.accessioned | 2026-07-07T04:43:38Z | |
| dc.date.available | 2026-07-07T04:43:38Z | |
| dc.description | A classification of finite dimensional irreducible representations of the nonstandard $q$-deformation $U'_q(so_n)$ of the universal enveloping algebra $U(so(n, C))$ of the Lie algebra $so(n, C)$ (which does not coincides with the Drinfeld--Jimbo quantized universal enveloping algebra $U_q(so_n)$) is given for the case when $q$ is not a root of unity. It is shown that such representations are exhausted by representations of the classical and nonclassical types. Examples of the algebras $U'_q(so_3)$ and $U'_q(so_4)$ are considered in detail. The notions of weights, highest weights, highest weight vectors are introduced. Raising and lowering operators for irreducible finite dimensional representations of $U'_q(so_n)$ and explicit formulas for them are given. They depend on a weight upon which they act. Sketch of proofs of the main assertions are given. | |
| dc.description | 13 pages, LaTeX. Report on Int. Conf. on Functional Analysis (Kiev, August 2001) | |
| dc.identifier | https://arxiv.org/abs/math/0110038 | |
| dc.identifier | http://arxiv.org/abs/math/0110038 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62312 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | Classification of irreducible representations of the q-deformed algebra U'_q(so_n) | |
| dc.type | text |