Introduction to Group Representation Theory

What it is about

You will receive an introduction to the representation theory of groups and algebras with a view to applications in mathematics and the natural sciences. In the end you will be able to apply fundamental techniques such as complete reducibility, character theory and the representation of symmetric groups (or alternatively Hecke algebras and braid groups) and to explore further areas.

What you will be able to do

• Understanding representations of algebras: equivalence, complete reducibility, characters
• Applying group algebras and Maschke's theorem
• Using the orthogonality relations of the characters
• Applying representation methods to classical results of group theory and invariant theory
• Basic knowledge on representations of symmetric groups or on Hecke algebras and braid groups

What the module consists of

• VorlesungDelivery of the theoretical content through examples and discussions
• Übung/Practice SessionsDeepening the lecture content through problem sheets, solutions and independent understanding checks

Teaching method

• Vortrag mit Beispielen und Diskussionpresents the content and motivates own analysis
• Übungsblätter mit Lösungen in begleitenden Übungssitzungenenables the deepening of methods and verification of learning success