Jacquet modules and the Langlands classification

Abstract

Abstract. In this paper, we consider a standard module in the subrepresentation setting of the Langlands classification. We show that the inducing representation appears with multiplicity one in the corresponding Jacquet module, and in fact, it is the unique subquotient of the Jacquet module with its central exponent. As an application, we show how this may be used to easily deduce a dual Langlands classification–essentially, a generalization of the Zelevinsky classification for general linear groups. 1.