Degenerate series representations of the \(q\)-deformed algebra \(\text{so}_q'(r,s)\)

DOI10.3842/SIGMA.2007.064zbMATH Open1161.17007arXiv0705.0276MaRDI QIDQ2473463

Publication date: 27 February 2008

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Abstract: The q-deformed algebra

m s o'_{q} (r, s)

is a real form of the q-deformed algebra

U'_{q} (m s o (n, m a t h b b C))

,

n = r + s

, which differs from the quantum algebra

U_{q} (m s o (n, m a t h b b C))

of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra

m s o'_{q} (r, s)

. The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra

m s o'_{q} (r) i m e s m s o'_{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

m s o'_{q} (r, s)

are separated in the set of irreducible representations obtained in the paper.

Full work available at URL: https://arxiv.org/abs/0705.0276

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zbMATH Keywords

irreducible representations reducible representations \(s\)-deformed algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)