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Norm-square localization and the quantization of Hamiltonian loop group spaces
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-05-01 , DOI: 10.1016/j.jfa.2019.108445
Yiannis Loizides , Yanli Song

Abstract In an earlier article we introduced a new definition for the ‘quantization’ of a Hamiltonian loop group space M , involving the equivariant L 2 -index of a Dirac-type operator D on a non-compact finite dimensional submanifold Y of M . In this article we study a deformation of this operator, similar to the work of Tian-Zhang and Ma-Zhang. We obtain a formula for the index with infinitely many non-trivial contributions, indexed by the components of the critical set of the norm-square of the moment map. This is the main part of a new proof of the [ Q , R ] = 0 theorem for Hamiltonian loop group spaces.

中文翻译:

范数平方定位和哈密顿循环群空间的量化

摘要 在较早的一篇文章中,我们介绍了哈密顿循环群空间 M 的“量化”的新定义,涉及 M 的非紧致有限维子流形 Y 上的狄拉克型算子 D 的等变 L 2 -索引。在这篇文章中,我们研究了这个算子的变形,类似于 Tian-Zhang 和 Ma-Zhang 的工作。我们获得了一个具有无限多非平凡贡献的指数的公式,由矩图的范数平方的临界集的分量索引。这是哈密顿循环群空间的 [ Q , R ] = 0 定理的新证明的主要部分。
更新日期:2020-05-01
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