Representation Theory    (Winter Semester 2014/15)

The course is addressed to Master students or Phase I BMS Students. 
Since the course is registered as a BMS course, it will be hold in English (unless audience prefers German or Spanish language )

The contents of the course:

1. Representations of finite groups
- Irreducibility and G-homorphisms (Schur's Lemma)
- Tensor, dual and induced representations
- Permutation representations
- Examples: Representation symmetric and alternating groups

2. Character theory
- Characters and class functions
- Character tables
- Reciprocity formulae

3. Representations of the symmetric group
- Irreducible representations and Young Diagrams
- Frobenius formula

4. Schur Functors

5. The group algebra

6. Induced representations
- Mackey´s irreducibility criterion
- Examples of induced representations

I will follow mostly the book of Harris-Fulton "Representation Theory, a first course"  (GTM 129, Springer)
and J.-P. Serre´s  "Linear Representations of Finite Groups"
( GTM 42, Springer ) . Eventually I will use
the Fulton's book "Young Tableaux"  (LMS Student Texts 35)

The prerequisites are the courses of Linear Algebra and  Algebra.

For the moment there is no exercises session but I will leave exercises every week to
work them out.


Sheet 1 (21.04)
Sheet 2 (03.05)
Sheet 3 (14.05)

Sheet 4 (27.05)
Sheet 5 (06.06)
Sheet 6 (25.06)