The Atiyah-Bott Lefschetz Formula Applied to the Based Loops on SU(2)

Abstract

The Atiyah-Bott Lefschetz Formula is a well-known formula for computing the equivariant index of an elliptic operator on a compact smooth manifold. We provide an analogue of this formula for the based loop group $\Omega SU(2)$ with respect to the natural $(T\times S^1)$-action. From this result we also derive an effective formula for computing characters of certain Demazure modules.

Revised version based on referee's recommendations

References in corpus (2)

• The T-equivariant Cohomology of Bott-Samelson varieties
• Notes on Schubert classes of a loop group