Summer Lectures in Geometry   RSS

29/06/2011, 11:00 — 12:00 — Room P3.10, Mathematics Building
, Johns Hopkins and UCSD

Geometry, Topology and Representation Theory of Loop Groups

In this sequence of three talks, I will aim to introduce the algebraic and geometric structure of Loop groups and their representations. We will begin with the basic structure of Affine Lie algebras. This will lead us to the algebraic theory of positive energy representations indexed by the level. On the geometric side, we will introduce the Affine Loop group and relate it to the central extension of the smooth loop group. We will also study the example of the special unitary group in some detail. In the remaining time, I will go into some of the deeper structure of Loop groups. This includes fusion in the representations of a given level (via the geometric notion of conformal blocks). Time permitting, I will also describe the homotopy type of the classifying space of Loop groups. No special background is required. It would be helpful to know the basic theory of root systems for semisimple Lie algebras, though this is not a strict requirement.


See also

For detailed overviews of each course see