Representations of the q-deformed algebra $U'_q(so_{2,2})$

A. U. Klimyk

paper

Representations of the q-deformed algebra $U_{q}^{'} (s o_{2, 2})$

arXiv:q-alg/9709035

Abstract

The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible $*$ -representations of the q-deformed algebra $U_{q}^{'} (s o_{2, 2})$ which is a real form of the non-standard deformation $U_{q}^{'} (s o_{4})$ of the universal enveloping algebra $U (so (4, C))$ . These representations are described by two complex parameters and are obtained by "analytical continuation" of the irreducible finite dimensional representations of the algebra $U_{q}^{'} (s o_{4})$ in the basis corresponding to the reduction from $U_{q}^{'} (s o_{4})$ to $U (s o_{2} \oplus s o_{2})$ .

arXiv comment15 pages, LaTeX

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Representations of the q-deformed algebra $U_{q}^{'} (s o_{2, 2})$