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arXiv math/0610895math.RT
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关于量子群$U_{q}(f_{m}(K,H))$的表示

On representations of quantum groups $U_{q}(f_{m}(K,H))$

Xin Tang, Yunge Xu

备注：
Some minor modifications to the first version
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摘要：

构造了一类量子群$U_{q}(f_{m}(K,H)$的不可约表示族.首先，我们将这些量子群实现为双曲代数。这样的实现产生$U_{q}(f_{m}(K,H))$的不可约权表示的自然族。其次，我们研究了$U_{q}(f_{m}(K,H))$和$U_{q}(f_{m}(K))$之间的关系。证明了$U_{q}(f_{m}(K,H))$的任意有限维权表示都是完全可约的。最后，研究了$U_{q}(f_{m}(K,H))$中心的Whittaker模型，得到了$U_{q}(f_{m}(K,H))$的不可约Whittaker表示的分类.

英文摘要：

We construct families of irreducible representations for a class of quantum groups $U_{q}(f_{m}(K,H)$. First, we realize these quantum groups as Hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for $U_{q}(f_{m}(K,H))$. Second, we study the relationship between $U_{q}(f_{m}(K,H))$ and $U_{q}(f_{m}(K))$. As a result, any finite dimensional weight representation of $U_{q}(f_{m}(K,H))$ is proved to be completely reducible. Finally, we study the Whittaker model for the center of $U_{q}(f_{m}(K,H))$, and a classification of all irreducible Whittaker representations of $U_{q}(f_{m}(K,H))$ is obtained.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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