Location BA1200
The free loop group of a compact Lie group has a very interesting representation theory, related to modular forms, integrable systems, quantum groups, vertex algebras, string theory... Of particular interest is the fusion product of representations. The representation theory of the *based* loop groups have never been considered before (even though individual examples of representations have been considered in disguise). We will explain how to extend the fusion product to representations of the based loop groups, and how to recover the category of representations of the free loop group from the category of representations of the based loop group. At last, I will explain in what sense I expect the representation theory of based loop groups to be wild (unlike that of the based loop groups), and which representations one might have a hope to classify.