Memoirs of the American Mathematical Society 1993; 111 pp; softcover Volume: 102 ISBN10: 0821825496 ISBN13: 9780821825495 List Price: US$38 Individual Members: US$22.80 Institutional Members: US$30.40 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 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. 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
