Instructor: Dr. Péter Pál Pálfy

Text: I. Martin Isaacs, Character Theory of Finite Groups

Prerequisite: A course in abstract algebra including basic group theory, ring theory and Galois theory, plus linear algebra.

Course description: Representation theory studies how groups appear as groups of linear transformations (or groups of matrices). This course will be restricted to the classical case, the study of representations of finite groups over the complex field. The basic tool is the character of a representation, a complex valued function defined on the group. The beautiful theory of characters is applied to prove important results in group theory such as the solvability of groups of order divisible by only two distinct primes.

Topics: Algebras, modules, and representations
Group representations and characters
Characters and algebraic integers
Products of characters
Induced characters
Characters of normal subgroups
Trivial intersection sets and exceptional characters
Brauer's characterization of characters
Projective representations
Results on linear groups