Thursday, October 31, 2024, 03:30pm - 04:30pm
For a certain class of real analytic varieties with Lie group actions I will develop a theory of (free-monodromic) tilting sheaves, and apply it to flag varieties stratified by real group orbits. For quasi-split real groups, I'll construct a fully faithful embedding of the category of tilting sheaves to a real analog of the category of Soergel bimodules, establishing real group analogs of Soergel's Structure Theorem and Endomorphism Theorem. As an application of these results I'll give a purely geometric proof of the theorem of Bezrukavnikov and Vilonen which proves Soergel's conjecture for quasi-split groups. The talk is based on the joint work with Zhiwei Yun.
Location: PMA 12.166