
SIGMA 3 (2007), 064, 12 pages arXiv:0705.0276
https://doi.org/10.3842/SIGMA.2007.064
Degenerate Series Representations of the qDeformed 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 qdeformed algebra so'_{q}(r,s) is a real
form of the qdeformed algebra U_{q}'(so(n,C)),
n = r + s, which differs from the quantum algebra
U_{q}(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:
qdeformed algebras; irreducible representations; reducible representations.
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