等变K-理论的Witten非阿贝尔局部化及[Q，R]=0定理
Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem
摘要：
本文件有两个目的。首先，当M是任意偶数维紧流形时，我们得到了一个非交换局部化定理：Witten，我们变形一个椭圆符号的Clifford丛与一个向量场相关的矩映射。其次，我们利用这个一般方法在Hamilton情形下重新证明了Meinrenken-Sjamaar的[Q，R] = 0定理，并得到了对殆复流形的温和推广.这个非阿贝尔定域定理可以用来获得一般自旋^c狄拉克算子指数重数的几何描述（见预印本arXiv：1411.7772）。
英文摘要：
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 localization theorem can be used to obtain a geometric description of the multiplicities of the index of general spin^c Dirac operators (see preprint arXiv:1411.7772).
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