# セミナー

## 微分幾何・トポロジーセミナー

タイトル Geometric Quantization and Foliation Reduction 2013年6月24日 17：15-18：15 Paul Skerritt (California Institute of Technology) 慶應義塾大学理工学部　14棟631A A standard question in the study of geometric quantization, dating back to the work of Guillemin and Sternberg in the early 1980s, is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether quantization commutes with reduction.'' In this talk I will propose a notion of prequantum reduction'', and discuss how it and symplectic reduction can be viewed in a unified framework as special cases of foliation reduction. For compact Lie group symmetries, consistency of prequantum reduction then implies Bohr-Sommerfeld-like conditions on the associated momenta. After introducing a polarization compatible with prequantum reduction, I will discuss the full geometric quantization of the system. The underlying symplectic geometry induces a decomposition of the space of polarized sections, which demonstrates that quantization and reduction do indeed commute in this context.