Induced representations and the Langlands classification

Abstract

In these lecture notes 1 we discuss the concept of induction and some of its applications to the representation theory of a real semisimple Lie group. In particular, we give an introduction to parabolic induction, Bruhat theory, the asymptotic behavior of matrix coecients, the subrepresentation theorem, characterization of discrete series and tempered representations, and, nally, the Langlands classication of irreducible admissible representations.