English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The q-deformed algebra ${\rm so}'_q(r,s)$ is a real form of the q-deformedalgebra $U'_q({\rm so}(n,\mathbb{C}))$, $n=r+s$, which differs from the quantumalgebra $U_q({\rm so}(n,\mathbb{C}))$ of Drinfeld and Jimbo. We studyrepresentations of the most degenerate series of the algebra ${\rmso}'_q(r,s)$. The formulas of action of operators of these representations uponthe basis corresponding to restriction of representations onto the subalgebra${\rm so}'_q(r)\times {\rm so}'_q(s)$ are given. Most of these representationsare irreducible. Reducible representations appear under some conditions for theparameters determining the representations. All irreducible constituents whichappear in reducible representations of the degenerate series are found. All$*$-representations of ${\rm so}'_q(r,s)$ are separated in the set ofirreducible representations obtained in the paper.

Degenerate Series Representations of the $q$-Deformed Algebra ${\rm so}'_q(r,s)$