%0 Journal Article
%T Remark on representation theory of general linear groups over a non-archimedean local division algebra
%A Tadi£¿
%A Marko
%J -
%D 2015
%X Sa£¿etak In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the irreducible square integrable representations of these groups by segments of cuspidal representations, and a proof of the irreducibility of the tempered parabolic induction. Our proofs are based on Jacquet modules (and the Geometric Lemma, incorporated in the structure of a Hopf algebra). We use only some very basic general facts of the representation theory of reductive p-adic groups (the theory that we use was completed more then three decades ago, mainly in 1970-es). Of the specific results for general linear groups over A, basically we use only a very old result of G. I. Ol¡¯£¿anskii, which says that there exist complementary series starting from Ind(¦Ñ £¿ ¦Ñ) whenever ¦Ñ is a unitary irreducible cuspidal representation. In appendix of [11], there is also a simple local proof of these results, based on a slightly different approach
%K Non-archimedean local fields
%K division algebras
%K general linear groups
%K Speh representations
%K parabolically induced representations
%K reducibility
%K unitarizability
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=213817