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Degenerate Principal Series for Symplectic Groups
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Memoirs of the American Mathematical Society
1993; 111 pp; softcover
Volume: 102
ISBN-10: 0-8218-2549-6
ISBN-13: 978-0-8218-2549-5
List Price: US$36 Individual Members: US$21.60
Institutional Members: US\$28.80
Order Code: MEMO/102/488

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.

• Notation and preliminaries
• The Hecke algebra approach
• Irreducibility of certain representations á la Tadić
• Irreducibility criteria for degenerate principal series in $$SP_4(F)$$, $$SP_6(F)$$, á la Tadić
• Appendix