The parabolic exotic t-structure

Pramod N Achar (1) , Nicholas Cooney (2, 3) , Simon Riche (2, 3)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]

Let G be a connected reductive algebraic group over an algebraically closed field k, with simply connected derived subgroup. The exotic t-structure on the cotangent bundle of its flag variety T^*(G/B), originally introduced by Bezrukavnikov, has been a key tool for a number of major results in geometric representation theory, including the proof of the graded Finkelberg-Mirkovic conjecture. In this paper, we study (under mild technical assumptions) an analogous t-structure on the cotangent bundle of a partial flag variety T^*(G/P). As an application, we prove a parabolic analogue of the Arkhipov-Bezrukavnikov-Ginzburg equivalence. When the characteristic of k is larger than the Coxeter number, we deduce an analogue of the graded Finkelberg-Mirkovic conjecture for some singular blocks.

Domaines: Théorie des représentations [math.RT]

Pramod N Achar, Nicholas Cooney, Simon Riche. The parabolic exotic t-structure. 2018. ⟨hal-01788372v1⟩