THE ALGEBRAIC THEORY OF TEMPERED REPRESENTATIONS OF p-ADIC GROUPS I. PARABOLIC INDUCTION AND RESTRICTION

Abstract

In this paper we study the category of non-degenerate modules over the Harish-Chandra Schwartz algebra of a p-adic connected reductive group. We construct functors of parabolic induction and restriction and show that they are exact and both ways adjoint to each other.