ENGLISH

Degenerate Principal Series for Symplectic Groups

By Chris Jantzen

Book information

Publisher
Amer Mathematical Society
Year
1993
ISBN
0821825496, 9780821825495
Language
english
Format
PDF
Filesize
7 MB (7690503 bytes)
Series
Memoirs of the American Mathematical Society
Pages
111\130
DPI
600
Orientation
yes
Scanned
yes
Time added
2014-09-08 01:32:25

Description

This paper is concerned with induced representations for $p$-adic groups. In particular, Jantzen examines the question of reducibility in the case where the inducing subgroup is a maximal parabolic subgroup of $Sp_{2n}(F)$ and the inducing representation is one-dimensional. Two different approaches to this problem are used. The first, based on the work of Casselman and of Gustafson, reduces the problem to the corresponding question about an associated finite-dimensional representation of a certain Hecke algebra. The second approach is based on a technique of Tadic and involves an analysis of Jacquet modules. This is used to obtain a more general result on induced representations, which may be used to deal with the problem when the inducing representation satisfies a regularity condition. The same basic argument is also applied in a case-by-case fashion to nonregular cases.

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