Classification theorem on irreducible representations of the q-deformed algebra U'_q(so(n))
Quantum Algebra
2007-05-23 v1 Representation Theory
Abstract
The aim of this paper is to give a complete classification of irreducible finite dimensional representations of the nonstandard q-deformation U'_q(so(n)) (which does not coincide with the Drinfeld-Jimbo quantum algebra U_q(so(n)) of the universal enveloping algebra U(so(n,C)) of the Lie algebra so(n,C) when q is not a root of unity. These representations are exhausted by irreducible representations of the classical type and of the nonclassical type. Theorem on complete reducibility of finite dimensional representations of U'_q(so(n)) is proved.
Keywords
Cite
@article{arxiv.math/0702482,
title = {Classification theorem on irreducible representations of the q-deformed algebra U'_q(so(n))},
author = {N. Z. Iorgov and A. U. Klimyk},
journal= {arXiv preprint arXiv:math/0702482},
year = {2007}
}
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29 pages