Welcome
Welcome to the webpage of the mastermath course "Representation theory". If you are interested in following the course, please fill in this form.
Aim
In this course we study linear representations of finite groups. Our approach is to present the basic ideas of the theory in a reasonably general context. We do not prove the basic results purely for group representations, but rather for the appropriate sort of rings and modules, deriving the results for group representations from them.
Description
A (linear) representation of a group is a homomorphism from the group to a group of linear transformations of a vector space. Every group admits such representations, and even faithful ones. In this course we focus on the theory of representations of finite groups. This theory can be divided into two parts: ordinary representation theory, the case where the characteristic of the field is 0 or prime to the order of the group, and modular representation theory, the case where the characteristic of the field divides the order of the group. We will mainly be concerned with ordinary representation theory. We will apply the results from representation theory to general group theory. For example, we prove Frobenius' Theorem and Burnside's famous paqb-theorem, stating that every finite group of order paqb, with p and q prime, is solvable.
