Some quantum analogues of solvable Lie groups
Some quantum analogues of solvable Lie groups
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发表时间：
1993-08
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通讯作者：
C. Concini;V. Kac;C. Procesi
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作者：
C. Concini;V. Kac;C. Procesi
本文分析了单李群G的幂单可解子群所对应的量子包络代数的某些子代数的结构。这些代数的非交换结构的迭代代数扭曲多项式的导子，一个对象，经常出现在一般理论的非交换环。特别是，我们发现他们的不可约表示的最大尺寸。我们的结果证实了一般哲学的有效性，表示理论是密切相关的泊松几何。
In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras of twisted polynomials with a derivation, an object which has often appeared in the general theory of non-commutative rings. In particular, we find maximal dimensions of their irreducible representations. Our results confirm the validity of the general philosophy that the representation theory is intimately connected to the Poisson geometry.