On supports of induced representations for symplectic and odd-orthogonal groups
On supports of induced representations for symplectic and odd-orthogonal groups
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关于辛和奇正交群的诱导表示的支持
DOI：
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发表时间：
1997
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通讯作者：
Chris Jantzen
中科院分区：
文献类型：
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作者：
Chris Jantzen
设G是Sp（2 n，F）（resp. SO（2n + 1，F）），其中F是特征为零的p-adic域.本文给出了G的一个不可约表示π与一个低秩辛不可约表示的m -元组（分别为π、π正交）群基于π的超尖点支撑。我们表明，这种对应尊重归纳和雅凯模函子（在某种意义上要精确），以及验证一些其他有用的属性。本质上，这种对应允许人们隔离一般线性群的超尖点表示的不同族的影响，这些超尖点表示出现在π的支持下。
Let G be Sp (2 n, F ) (resp. SO (2 n + 1, F )), where F is a p -adic field of characteristic zero. In this paper, we give a correspondence which associates to an irreducible representation π of G an m -tuple of irreducible representations of lower rank symplectic (resp. orthogonal) groups based on the supercuspidal support of π. We show that this correspondence respects the induction and Jacquet module functors (in a sense to be made precise), as well as verifying a number of other useful properties. In essence, this correspondence allows one to isolate the effects of the different families of supercuspidal representations of general linear groups which appear in the support of π.