A Topic in Representation Theory

In representation theory of finite groups, there are three types of
behaviour: finite, tame and wild. The finite case has been largely understood, and the next least complicated is tame. Here there are strong theorems, butstill some open questions.

This project aims to answer some of these questions. In the 1980s, Karin Erdmann gave a list of the possible tame structures, but not all from her list appear in finite groups. We will start by using the classification of finite simple groups to restict beyond Erdmann's list the possible tame structures, hopefully to the exact list of tame structures that appear in finite groups. Second, we will look at the quaternionic structure, where although it is known that the objects in the structure are classifiable, no classification is known. Using modern computer techniques and the covering semidihedral structure (whose objects were classified by William Crawley-Boevey), we aim to produce first conjectures as to the objects in the quaternionic structure, and then to prove that these conjectures are correct.