# 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.

Exercises:

Sheet 1 (21.04)

Sheet
2 (03.05)

Sheet 3 (14.05)

Sheet 4 (27.05)

Sheet 5 (06.06)

Sheet
6 (25.06)

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