
Journal of Lie Theory 26 (2016), No. 1, 135168 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 imatic@mathos.hr 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 εfunction 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 squareintegrable representation on the general linear part. Keywords: Discrete series, classical padic groups, Jacquet modules. MSC: 22E35; 22E50 [ Fulltextpdf (403 KB)] for subscribers only. 