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

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

1997-09-23

arxiv.org/abs/q-alg/9709035v1

Mathematics

Quantum Algebra

15 pages, LaTeX

Scientific paper

The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible $*$-representations of the q-deformed algebra $U'_q(so_{2,2})$ which is a real form of the non-standard deformation $U'_q(so_4)$ 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 $U'_q(so_4)$ in the basis corresponding to the reduction from $U'_q(so_4)$ to $U(so_2\oplus so_2)$.

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