| Summary: | The $q$-deformed algebra ${m so}'_q(r,s)$ is a realform of the $q$-deformed algebra $U'_q({m so}(n,mathbb{C}))$,$n=r+s$, which dif/fers from the quantum algebra $U_q({mso}(n,mathbb{C}))$ of Drinfeld and Jimbo. We study representationsof the most degenerate series of the algebra ${m so}'_q(r,s)$. Theformulas of action of operators of these representations upon thebasis corresponding to restriction of representations onto thesubalgebra ${m so}'_q(r)imes {m so}'_q(s)$ are given. Most ofthese representations are irreducible. Reducible representationsappear under some conditions for the parameters determining therepresentations. All irreducible constituents which appear inreducible representations of the degenerate series are found. All$*$-representations of ${m so}'_q(r,s)$ are separated in the setof irreducible representations obtained in the paper.
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