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Journal of Lie Theory 22 (2012), No. 4, 1109--1124
Copyright Heldermann Verlag 2012

A Method of Proving Non-Unitarity of Representations of p-adic Groups

Marcela Hanzer
Dept. of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia

Chris Jantzen
Dept. of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A.

The authors study irreducible subquotients of a certain class of induced representations of classical p-adic 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 p-adic groups.

Keywords: Classical p-adic groups, generalized Steinberg representation, unitary representations, non-unitarity criterion.

MSC: 22E35, 22E50, 11F70

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