A note on harish-chandra induction
A note on harish-chandra induction
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关于 harish-chandra 归纳法的注释
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
Meinholf Geck
中科院分区：
文献类型：
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作者：
Meinholf Geck
R.B.Howlett和G.I.Lehrer得到了有限域上约化群的诱导尖点表示的自同态代数的详细描述。他们证明（并在许多情况下证明），这个代数总是同构于某个有限群的群代数。这个猜想等价于导出表示包含一个重数为1的不可约成分的陈述。卢斯蒂格（G.Lusztig）已经证明，对于具有连接中心的群体来说，这是正确的。本文用度刻画了重数为I的不可约成分，并利用正则嵌入和Clifford理论，从这个结果中推出Howlett猜想和LehreFs猜想一般成立.
R.B.Howlett and G.I.Lehrer obtained a detailed description of the endo-morphism algebra of an induced cuspidal representation of a reductive group over a finite field. They conjectured (and proved in many cases) that this algebra is always isomorphic to the group algebra of a certain finite group. This conjecture is equivalent to the statement that the induced representation contains an irreducible constituent with multi-plicty 1. G.Lusztig has shown that this is true for groups with connected centre. In this note, we characterize such an irreducible constituent with multiplicity I by its degree and deduce from this result, using regular embeddings and Clifford theory, that Howlett's and LehreFs conjecture holds in general.