| eBook 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 |
| eBook 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 102; 1993; 111 ppMSC: 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.
ReadershipResearch mathematicians.
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Table of Contents
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Chapters
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1. Notation and preliminaries
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2. The Hecke algebra approach
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3. Irreducibility of certain representations á la Tadić
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4. Irreducibility criteria for degenerate principal series in $SP_4(F)$, $SP_6(F)$, á la Tadić
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Appendix
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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 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
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Appendix
