Dirac operators on quasi-Hamiltonian G-spaces

Abstract

We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group. This generalizes the quantization of Hamiltonian $G$-spaces to quasi-Hamiltonian G-spaces.

All comments are welcome

References in corpus (1)

• Kac-Moody and Virasoro algebras

Cited by in corpus (2)

• An infinite-dimensional index theorem and the Higson-Kasparov-Trout algebra
• Topological Aspects of the Equivariant Index Theory of Infinite-Dimensional LT-Manifolds