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

作者：Hanzer Marcela^*; Jantzen Chris

来源：Journal of Lie Theory, 2012, 22(4): 1109-1124.

• Classical p-adic groups
• generalized Steinberg representation
• unitary representations
• non-unitarity criterion

In this paper the authors study irreducible subquotients of the 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%26apos;s results in the case of classical p-adic groups.

• 出版日期2012