MIT Lie Groups Seminar
Wednesday, September 20, 2023 at 4:00pm to 5:00pm
Building 2, 2-142
182 MEMORIAL DR, Cambridge, MA 02139
Speaker: Huanchen Boa (Singapore)
Title: Symmetric subgroup schemes, Frobenius splittings, and quantum symmetric pairs
Abstract : Let G be a connected reductive group over an algebraically closed field. Such groups are classified via root data and can be parameterised via Chevalley group schemes over integers. In this talk, we shall first recall the construction of Chevalley group schemes by Lusztig using quantum groups. Then we shall discuss the construction of symmetric subgroup schemes parameterising symmetric subgroups K of G using quantum symmetric pairs. The existence of such group schemes allows us to apply characteristic p methods to study the geometry of K-orbits on the flag variety of G. This leads to a construction of Frobenius splittings via quantum symmetric pairs, generalising the algebraic Frobenius splittings by Kumar-Littelmann. This is based on joint work with Jinfeng Song (NUS).