Lecture MA5134: Introduction to Group Representation Theory

Contents:
Representations of groups feature in many areas of mathematics besides algebra: they are indispensable tools in topology, combinatorics and advanced analysis, for example, and they also see much use outside mathematics, e.g., in chemistry and in theoretical physics. This module provides a thorough introduction to group representation theory and some of its applications. An outline of the specific topics is as follows:
• Representations of algebras: equivalence, complete reducibility, characters
• Representations of groups: group algebras, Maschke’s Theorem, orthogonality relations of characters
• Applications of group representations: some classical theorems from group theory and invariant theory
• Representations of symmetric groups or, alternatively, Hecke algebras and braid groups.

Literature:
M. Lorenz: A Tour of Representation Theory, Amer. Math. Soc., 2018

(Recommended) requirements:
For a successful participation in this module, familiarity with the rudiments of modern abstract algebra (MA2010 or MA2101) is required: basic group theory, theoretical linear algebra, rings and modules, and (finite) Galois theory.

Module level: Master         Language: English

Dates: The lecture will take place during May and June. The first lecture is on Tuesday, May 3, 2022. Please check TUMonline for the complete list of dates.