Witten Non Abelian Localization for Equivariant K-theory, and the $[Q,R]=0$ Theorem (Memoirs of the American Mathematical Society)

Paradan, Paul-Emile/ Vergne, Michele

American Mathematical Society（2020/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 71 p.
• 言語 ENG
• 商品コード 9781470435226
• DDC分類 512.66

Full Description

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 multiplicities of the index of general $spin^c$ Dirac operators.

Contents

Introduction
Index theory
$\mathbf{K}$-theoretic localization
``Quantization commutes with reduction'' theorems
Branching laws
Bibliography.