Mirror symmetry for special nilpotent orbit closures

：付保华（中科院数学院）
：2022-12-15 15:00
：腾讯会议ID：909-369-472（无密码）

报告人：付保华（中科院数学院）

时  间：12月15日下午15:00-16:30

地  点：腾讯会议ID：909-369-472（无密码）

内容摘要:

Motivated by geometric Langlands, we initiate a program to study the mirror symmetry between nilpotent orbit closures of a semisimple Lie algebra and those of its Langlands dual.

The most interesting case is Bn via Cn. Classically, there is a famous Springer duality between special orbits. Therefore, it is natural to speculate that the mirror symmetry we seek may coincide with Springer duality in the context of special orbits. Unfortunately, such a naive statement fails. To remedy the situation, we propose a conjecture which asserts the mirror symmetry for certain parabolic/induced covers of special orbits. Then, we prove the conjecture for Richardson orbits and obtain certain partial results in general. In the process, we reveal some very interesting and yet subtle structures of these finite covers, which are related to Lusztig’s canonical quotients of special nilpotent orbits. For example, there is a mysterious asymmetry in the footprint or range of degrees of these finite covers. Finally, we provide two examples to show that the mirror symmetry fails outside the footprint.

个人简介：

付保华，中国科学院数学与系统科学研究院研究员，主要从事代数几何的研究。曾获国家自然科学基金委杰出青年科学基金项目资助，入选国家高层次人才特殊支持计划以及中国科学院第十二届杰出青年，2019年获ICCM数学银奖。

 

联系人：余世霖