Classification theorem on irreducible representations of the q -deformed algebra U ′ q ( so n )

N. Z. Iorgov and A. U. Klimyk

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-38

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 Drinfel'd-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. The theorem on complete reducibility of finite-dimensional representations of U ′ q ( so n ) is proved.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:580840

DOI: 10.1155/IJMMS.2005.225

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