The Enhanced Period Map and Equivariant Deformation Quantizations of Nilpotent Orbits  

作　　者：Shi Lin YU 

机构地区：[1]Department of Mathematics,School of Mathematical Sciences,Xiamen University,Xiamen 361005,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第3期885-934,共50页数学学报（英文版）

基　　金：Supported by China NSFC grants(Grant Nos.12001453 and 12131018);Fundamental Research Funds for the Central Universities(Grant Nos.20720200067 and 20720200071)。

摘　　要：In a previous paper,the author and his collaborator studied the problem of lifting Hamil-tonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie groups.Only even quantizations were considered there.In this paper,these results are generalized to the case of general quantizations with arbitrary periods.The key step is to introduce an enhanced version of the(truncated)period map defined by Bezrukavnikov and Kaledin for quantizations of any smooth sym-plectic variety X,with values in the space of Picard Lie algebroid over X.As an application,we study quantizations of nilpotent orbits of real semisimple groups satisfying certain codimension condition.

关 键 词：Coadjoint orbit method deformation quantization Harish-Chandra modules semisimple Liegroups 

分 类 号：O152.5[理学—数学]