学术报告(付保华 11.9)

Mirror symmetry for special nilpotent orbit closures

发布人:杨晓静 发布日期:2022-11-07
主题
Mirror symmetry for special nilpotent orbit closures
活动时间
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活动地址
Zoom:97110625774
主讲人
付保华 研究员 中国科学院数学与系统科学研究院
主持人
李长征

Abstract: 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 onjecture 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. This is a joint work with Yongbin Ruan and Yaoxiong Wen.