Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 064, 12 pages      arXiv:0705.0276      http://dx.doi.org/10.3842/SIGMA.2007.064

Degenerate Series Representations of the q-Deformed Algebra so'q(r,s)

Valentyna A. Groza
National Aviation University, 1 Komarov Ave., 03058 Kyiv, Ukraine

Received January 26, 2007, in final form April 18, 2007; Published online May 02, 2007

Abstract
The q-deformed algebra so'q(r,s) is a real form of the q-deformed algebra Uq'(so(n,C)), n = r + s, which differs from the quantum algebra Uq(so(n,C)) of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra so'q(r,s). The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra so'q(r) × so'q(s) are given. Most of these representations are irreducible. Reducible representations appear under some conditions for the parameters determining the representations. All irreducible constituents which appear in reducible representations of the degenerate series are found. All *-representations of so'q(r,s) are separated in the set of irreducible representations obtained in the paper.

Key words: q-deformed algebras; irreducible representations; reducible representations.

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