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Journal of Lie Theory 26 (2016), No. 1, 135--168
Copyright Heldermann Verlag 2016

On Jacquet Modules of Discrete Series: the First Inductive Step

Ivan Matic
Dept. of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia

The purpose of this paper is to determine Jacquet modules of discrete series which are obtained by adding a pair of consecutive elements to the Jordan block of an irreducible strongly positive representation such that the ε-function attains the same value on both elements. Such representations present the first inductive step in the realization of discrete series starting from the strongly positive ones. We are interested in determining Jacquet modules with respect to the maximal standard parabolic subgroups, with an irreducible essentially square-integrable representation on the general linear part.

Keywords: Discrete series, classical p-adic groups, Jacquet modules.

MSC: 22E35; 22E50

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