Representation Theory

A.Y. 2015/2016
6
Max ECTS
42
Overall hours
SSD
MAT/02
Language
English
Learning objectives
The course is an introduction to Representation and Character Theory for finite groups.
Expected learning outcomes
Knowledge of the basics of Representation Theory of finite groups, construction of complex charater tables of some "small" groups.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
In the course (6 credits) we present basic ideas of representation theory for finite groups.

1. Definitions and examples. Irreducible, reducible and completely reducible representations of finite groups.
2. Representations and modules. Simple and semisimple modules: characterizations.
3. Applications to the group algebra. Maschke's Theorem.
4. Characters of finite groups Basic definitions and properties, irreducible characters, orthogonality relations, linear characters.
5. Character tables. Examples.
6. Applications of Character Theory. Solubility criteria, Burnside's Theorem, existence of normal subgroups and how to determine them.
7. Product of representations.
8. Induced representations and characters. Frobenius' Theorem.
9. Representations of symmetric groups. Partitions and Young tableaux, degrees of the irreducible representations of .
MAT/02 - ALGEBRA - University credits: 6
Lessons: 42 hours