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Degenerate Principal Series for Symplectic Groups

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Electronic ISBN: 978-1-4704-0065-1
Product Code: MEMO/102/488.E
List Price: $38.00 MAA Member Price:$34.20
AMS Member Price: $22.80 Click above image for expanded view Degenerate Principal Series for Symplectic Groups Available Formats:  Electronic ISBN: 978-1-4704-0065-1 Product Code: MEMO/102/488.E  List Price:$38.00 MAA Member Price: $34.20 AMS Member Price:$22.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 1021993; 111 pp
MSC: Primary 22;

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 Tadić 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.

Research mathematicians.

• Chapters
• 1. Notation and preliminaries
• 2. The Hecke algebra approach
• 3. Irreducibility of certain representations á la Tadić
• 4. Irreducibility criteria for degenerate principal series in $SP_4(F)$, $SP_6(F)$, á la Tadić
• Appendix
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Volume: 1021993; 111 pp
MSC: Primary 22;

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 Tadić 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.

• 4. Irreducibility criteria for degenerate principal series in $SP_4(F)$, $SP_6(F)$, á la Tadić