Introduction to Representation Theory - Part 1/3
By Birgit Speh
Appears in collection : 2025 - T1 - Representation theory and noncommutative geometry
The 3 lectures are introduction to representation theory of reductive real Lie groups at the level of the book ”Representation theory of semisimple Lie groups: An overview based on examples” by A.W. Knapp. All the concepts and theorems will be illustrated by examples, but I will give references for the detailed proofs. In each lecture I will give some suggested homework and reading.
Lecture 1. We will introduce discuss the basic important concepts: Admissible representations, differentiable vectors, equivalence of representations, irreducible representations, unitary representations, (g, K)-modules. Time permitting we will also introduce Cartan subgroups, the Iwasawa decomposition and parabolic subgroups.
This is a basic introduction to representation theory of nonimpact Lie groups.
