Deformation Quantization of Coadjoint Orbits
发布时间：2021年03月10日
浏览次数：5606
发布者: He Liu
主讲人： Shilin Yu (Xiamen Uiniversity)
活动时间： 从 2021-03-11 11:00 到 12:00
场地： 北京国际数学研究中心，全斋全29教室
The "coadjoint orbit method" philosophy of Kirillov and Kostant suggests that there is a close connection between the unitary dual of a Lie group G, which is the set of all irreducible unitary representations of G, and the set of coadjoint orbits in the dual of its Lie algebra. Roughly, one expects that the representations arise as "quantizations" of certain vector bundles on the coadjoint orbits, which are naturally symplectic manifolds.
When the Lie group is a noncompact real semisimple group, both the unitary dual and the orbit method are far from being fully understood, yet a lot of deep and interesting mathematics have been developed to study this case. Vogan suggested the candidates for the vector bundles on the coadjoint orbits to be quantized, which he called admissible vector bundles. In this talk, we show that these admissible vector bundles indeed correspond to representations, with some exceptions. The tools used here are deformation quantization of symplectic varieties and their Lagrangian subvarieties.
The talk is based on a joint paper with Conan Leung and an ongoing joint work with Ivan Losev.
