The parabolic exotic t-structure

Pramod N. Achar, Louisiana State University
Nicholas Cooney, Université Clermont Auvergne
Simon Riche, Université Clermont Auvergne


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-Mirković 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-Mirković conjecture for some singular blocks. ∗ ∗