Geometric quantization for proper moment maps: the Vergne conjecture

• 成果类型: Article
• 署名作者: Ma, Xiaonan; Zhang, Weiping
• 署名单位: Universite Paris Cite; Nankai University; Nankai University
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-014-0108-3
• 发表日期: 2014
• 页码: 11-57
• 关键词: multiplicities formula; MANIFOLDS; Operators; index

摘要

We establish an analytic interpretation for the index of certain transversally elliptic symbols on non-compact manifolds. By using this interpretation, we establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a non-compact symplectic manifold with proper moment map. In particular, we present a solution to a conjecture of MichSle Vergne in her ICM 2006 plenary lecture.