An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg

• 成果类型: Article
• 署名作者: Tian, YL; Zhang, WP
• 署名单位: New York University; Nankai University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050223
• 发表日期: 1998
• 页码: 229-259
• 关键词: multiplicities formula; localization

摘要

We present a direct analytic approach to the Guillemin-Sternberg conjecture [GS] that 'geometric quantization commutes with symplectic reduction', which was proved recently by Meinrenken [M1], [M2] and Vergne [V1], [V2] et al. Besides providing a new proof of this conjecture, our methods also lead immediately to further extensions in various contexts.