Electronic ISBN:  9781470400651 
Product Code:  MEMO/102/488.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $22.80 

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 onedimensional. 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 finitedimensional 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 casebycase fashion to nonregular cases.
ReadershipResearch mathematicians.

Table of Contents

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


RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
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 onedimensional. 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 finitedimensional 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 casebycase 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