$q$ -变形代数${\rm so}'_q(r,s)$的退化级数表示
Degenerate Series Representations of the $q$-Deformed Algebra ${\rm so}'_q(r,s)$
摘要：
q-变形代数${\rm so}'_q(r,s)$是q-变形代数$U'_q({\rm so}(n,\mathbb{C}))$的实形式$n=r+s$，它不同于Drinfeld和Jimbo的量子代数$U_q({\rm so}(n,\mathbb{C}))$。研究了代数${\rm so}'_q(r,s)$的最退化级数的表示.给出了这些表示的算子在对应表示的限制到子代数${\rm so}'_q(r)\times {\rm so}'_q(s)$上的基上的作用公式。这些表示大多数是不可约的。可约表示在某些条件下出现，参数决定的表示。找到了退化级数的可约表示中出现的所有不可约分量，并将${\rm so}'_q(r,s)$的所有$*$ -表示分离到本文得到的不可约表示集中.
英文摘要：
The q-deformed algebra ${\rm so}'_q(r,s)$ is a real form of the q-deformed algebra $U'_q({\rm so}(n,\mathbb{C}))$, $n=r+s$, which differs from the quantum algebra $U_q({\rm so}(n,\mathbb{C}))$ of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra ${\rm so}'_q(r,s)$. The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra ${\rm so}'_q(r)\times {\rm so}'_q(s)$ 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 ${\rm so}'_q(r,s)$ are separated in the set of irreducible representations obtained in the paper.
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