A method of proving non-unitarity of representations of p-adic groups I

作者：Hanzer Marcela^*; Tadic Marko

来源：Mathematische Zeitschrift, 2010, 265(4): 799-816.

DOI：10.1007/s00209-009-0542-7

• Classical p-adic groups
• Generalized Steinberg representation
• Unitary representations
• Non-unitarity criterion

In this paper we exhibit a new method of proving non-unitarity of representations, based on semi simplicity of unitarizable representations. Non-unitarity is proved for a half of all irreducible representations of classical p-adic groups whose infinitesimal character is the same as the infinitesimal character of a generalized Steinberg representation (as defined in Tadic, Am J Math 120:159-210, 1998). Only the Steinberg representation and its Aubert dual are expected to be unitary here. In this way we partially generalize a result of Casselman to the case of classical groups. Our argument is completely different from Casselman's argument (which is hard to extend to this case). It requires a very limited knowledge of the inducing cuspidal representation.

• 出版日期2010-8