 
Summary: Representations of linear Lie
groups and applications
Salem Ben Said
(i) This course requires knowledge of the courses done by J.P. Anker and L.
Kamoun.
(ii) These lecture notes are written in english for the students to get use to
this language.
As one can see from the works of Euler and Gauss, mathematicians of previous
centuries did not only publish general theorems but also examples which they
might enjoyed and which might have educated the reader.
From Siegel [Gesammelte Abhandlungen IV, 1979]
Contents
Part 1. Basic Representation Theory of Linear Lie Groups 5
1. Lie algebras of linear Lie groups: A brief review 6
2. Representations of linear Lie groups 10
3. An application of Nelson's theorem 22
Part 2. Representations of SL(2, R), and Beyond 29
4. Basic properties of SL(2, R) and SU(1, 1) 30
5. Finite dimensional representation of SL(2, R) 38
6. An application: The wave equation 42
