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

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

2007-02-16

arxiv.org/abs/math/0702482v1

Int. J. Math. Math. Sci. vol.2005, No.2 (2005), 225-262

Mathematics

Quantum Algebra

29 pages

Scientific paper

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.

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