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Degenerate Principal Series for Symplectic Groups
Chris Jantzen
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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
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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.

Readership

Research mathematicians.

Table of Contents

  • 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
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