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Preprints, Working Papers, ... Year : 2018

The parabolic exotic t-structure

Abstract

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.
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Dates and versions

hal-01788372 , version 1 (09-05-2018)
hal-01788372 , version 2 (19-11-2018)

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