Degenerate Principal Series for Symplectic Groups

Degenerate Principal Series for Symplectic Groups

Chris Jantzen
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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.
Categorias:
Ano:
1993
Editora:
Amer Mathematical Society
Idioma:
english
Páginas:
111
ISBN 10:
0821825496
ISBN 13:
9780821825495
Série:
Memoirs of the American Mathematical Society
Arquivo:
PDF, 7.33 MB
IPFS:
CID , CID Blake2b
english, 1993
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