Journal of Symplectic Geometry

Volume 1 (2001)

Number 1

The Verlinde formula as fixed point formulas

Pages: 1 – 46

DOI: https://dx.doi.org/10.4310/JSG.2001.v1.n1.a1

Authors

A. Alekseev

E. Meinrenken

C. Woodward

Abstract

We express the index of the Spin_C-Dirac operator on symplectic quotients of a Hamiltonian loop group manifold in terms of fixed point data. As an application we prove Verlinde formulas for the Spin_C-quantization of moduli spaces of flat bundles over surfaces.

Published 1 January 2001