dorsal/arxiv
View Schemaq-deformed algebras $U_q(so_n)$ and their representations
| Authors | A. M. Gavrilik, N. Z. Iorgov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709036 |
| URL | https://arxiv.org/abs/q-alg/9709036 |
| Journal | Methods Func.Anal.Topol. 3, no.4, 51-63 (1997) |
Abstract
For the nonstandard $q$-deformed algebras $U_q(so_n)$, defined recently in terms of trilinear relations for generating elements, most general finite dimensional irreducible representations directly corresponding to those of nondeformed algebras $so(n)$ (i.e., characterized by the same sets of only integers or only half-integers as in highest weights of the latter) are given explicitly in a $q$-analogue of Gel'fand-Tsetlin basis. Detailed proof, for $q$ not equal to a root of unity, that representation operators indeed satisfy relevant (trilinear) relations and define finite dimensional irreducible representations is presented. The results show perfect suitability of the Gel'fand-Tsetlin formalism concerning (nonstandard) $q$-deformation of $so(n)$.
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"abstract": "For the nonstandard $q$-deformed algebras $U_q(so_n)$, defined recently in\nterms of trilinear relations for generating elements, most general finite\ndimensional irreducible representations directly corresponding to those of\nnondeformed algebras $so(n)$ (i.e., characterized by the same sets of only\nintegers or only half-integers as in highest weights of the latter) are given\nexplicitly in a $q$-analogue of Gel\u0027fand-Tsetlin basis. Detailed proof, for $q$\nnot equal to a root of unity, that representation operators indeed satisfy\nrelevant (trilinear) relations and define finite dimensional irreducible\nrepresentations is presented. The results show perfect suitability of the\nGel\u0027fand-Tsetlin formalism concerning (nonstandard) $q$-deformation of $so(n)$.",
"arxiv_id": "q-alg/9709036",
"authors": [
"A. M. Gavrilik",
"N. Z. Iorgov"
],
"categories": [
"q-alg",
"gr-qc",
"hep-th",
"math.QA"
],
"journal_ref": "Methods Func.Anal.Topol. 3, no.4, 51-63 (1997)",
"title": "q-deformed algebras $U_q(so_n)$ and their representations",
"url": "https://arxiv.org/abs/q-alg/9709036"
},
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