Slices in the loop spaces of symmetric varieties

Geometric Representation Theory Seminar

Organizers：

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker：

Lingfei Yi 易灵飞 (上海数学中心)

Time：

Wed., 3:30-4:30 pm, Sept. 25, 2024

Venue：

B627, Shuangqing Complex Building A

清华大学双清综合楼A座 B627

Title:

Slices in the loop spaces of symmetric varieties

Abstract：

Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.