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.