Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem

摘要: The purpose of the present paper is two-fold. First, we obtain a non-abelian localization theorem when M any even dimensional compact manifold : following an idea E. Witten, deform elliptic symbol associated to Clifford bundle on with vector field moment map. Second, use this general approach reprove [Q,R] = 0 Meinrenken-Sjamaar in Hamiltonian case, and mild generalizations almost complex manifolds. This can be used geometric description multiplicities index spin^c Dirac operators (see preprint arXiv:1411.7772).