Israel Journal of Mathematics

, Volume 107, Issue 1, pp 29–91

On reducibility of parabolic induction

Article

DOI: 10.1007/BF02764004

Cite this article as:
Tadić, M. Isr. J. Math. (1998) 107: 29. doi:10.1007/BF02764004

Abstract

Jacquet modules of a reducible parabolically induced representation of a reductivep-adic group reduce in a way consistent with the transitivity of Jacquet modules. This fact can be used for proving irreducibility of parabolically induced representations. Classical groups are particularly convenient for application of this method, since we have very good information about part of the representation theory of their Levi subgroups (general linear groups are factors of Levi subgroups, and therefore we can apply the Bernstein-Zelevinsky theory). In the paper, we apply this type of approach to the problem of determining reducibility of parabolically induced representations ofp-adic Sp(n) and SO(2n+1). We present also a method for getting Langlands parameters of irreducible subquotients. In general, we describe reducibility of certain generalized principal series (and some other interesting parabolically induced representations) in terms of the reducibility in the cuspidal case. When the cuspidal reducibility is known, we get explicit answers (for example, for representations supported in the minimal parabolic subgroups, the cuspidal reducibility is well-known rank one reducibility).

Copyright information

© The Magnes Press 1998

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ZagrebZagrebCroatia