
Journal of Lie Theory 22 (2012), No. 4, 11091124 Copyright Heldermann Verlag 2012 A Method of Proving NonUnitarity of Representations of padic Groups Marcela Hanzer Dept. of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia hanmar@math.hr Chris Jantzen Dept. of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A. jantzenc@ecu.edu The authors study irreducible subquotients of a certain class of induced representations of classical padic groups SO(2n+1,F) and Sp(2n,F). The induced representations in question are the ones which contain, as subquotients, generalized Steinberg and generalized trivial representation. We prove that the only unitarizable irreducible subquotients of the induced representations in question are precisely generalized Steinberg and generalized trivial representation, thus continuing the previous work of the first author and M. Tadic. This is, in a certain sense, a generalization of Casselman's results in the case of classical padic groups. Keywords: Classical padic groups, generalized Steinberg representation, unitary representations, nonunitarity criterion. MSC: 22E35, 22E50, 11F70 [ Fulltextpdf (327 KB)] for subscribers only. 