The Generalized Injectivity Conjecture for Classical p -Adic Groups

Abstract

We prove that the conjecture posed by Casselman and Shahidi, which says that a generic subquotient of a generic standard representation of a connected quasi-split reductive p-adic group is a subrepresentation (“generalized injectivity conjecture”), is valid in the case of classical groups with the generalized rank one standard representation. The generalized rank one case that we prove in this article is the key step in proving the claim in general, for every generic standard representation of a classical group.