Witten non abelian localization for equivariant K-theory, and the [Q, R]=0 theorem - Paradan, Paul-Emile; Vergne, Michèle (Memoirs of the American Mathematical Society., 2019)
The purpose of the present memoir is two-fold. First, the authors obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, the authors deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, the authors use this general approach to reprove the [Q, R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case and obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplici.