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

@article{Paradan2015WittenNA,
  title={Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem},
  author={P. Paradan and M. Vergne},
  journal={arXiv: Symplectic Geometry},
  year={2015}
}
The purpose of the present paper is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case, and we obtain mild generalizations to almost complex manifolds. This non-abelian… Expand
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