Geodesic
A Method of Proving Non-Unitarity of Representations of p-adic Groups
Marcela Hanzer1 ; Chris Jantzen2
1Dept. of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia
2Dept. of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A.
Journal of Lie Theory, Tome 22 (2012) no. 4, pp. 1109-1124

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22E35, 22E50, 11F70
Mots-clés : Classical p-adic groups, generalized Steinberg representation, unitary representations, non-unitarity criterion

Marcela Hanzer  1   ; Chris Jantzen  2

1 Dept. of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia
2 Dept. of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A. 
Marcela Hanzer; Chris Jantzen. A Method of Proving Non-Unitarity of Representations of p-adic Groups. Journal of Lie Theory, Tome 22 (2012) no. 4, pp. 1109-1124. http://geodesic.mathdoc.fr/item/JOLT_2012_22_4_a9/
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