Let G be a complex, connected, reductive, algebraic group, and χ : ℂ× → G be a fixed cocharacter that defines a grading on 𝔤, the Lie algebra of G. Let G0 be the centralizer of χ(ℂ×). Here I will talk about G0-equivariant parity sheaves on the n-graded piece, 𝔤n. For the first half we will spend on building the background of derived category of equivariant perverse sheaves, bijection between the simple objects and some pairs that we are familiar with. In positive characteristic parity sheaves will play an important role. We want to study DbG0(𝔤n, k) for characteristic of k is positive. For that we will dive into the results of Lusztig in characteristic 0 in the graded setting. The main result from Lusztig is that every perverse sheaf occurs as a direct summand of the parabolic induction of the simple perverse sheaf associated to some cuspidal pair. The goal of the second talk will be to extend this result into positive characteristic.
This is the first part of two talks, the second of which may be found here.
This video is part of the University of Georgia‘s Algebra seminar.
