The course will be an introduction to the representation theory of compact matrix Lie groups.  

We will be using the textbook: Analysis on Lie groups: An introduction by Jacques Faraut.

We will tentatively cover the following topics:

1. The linear group GL(n,R)

2. The exponential map

3. Linear Lie groups

4. Lie algebras

5. Haar measure

6. Representation theory of compact linear Lie groups

7. Representation theory of SU(2)
   
   

Lecture 1:  The linear group and some of its subgroups

Lecture 2. The exponential map (1)

Lecture 3: The exponential map (2)

Lecture 4. The exponential map (3)

Lecture 5.  Linear Lie groups and Lie algebras (1)

Lecture 6. Linear Lie groups and Lie algebras (2)

Lecture 7. Derived and adjoint representations

Lecture 8. The Lie group SU(2)

Lecture 9. The Haar measure on linear Lie groups

Lecture 10. Schur's lemmas

Lecture 11. Irreducible representations of SU(2)