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.

Source : oai:HAL:hal-01788372v2

Volume: Volume 2

Published on: November 21, 2018

Submitted on: May 22, 2018

Keywords: t-structure,exceptional collection,Flag varieties,derived category of coherent sheaves,parity complexes,
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MATH.MATH-RT
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Mathematics [math]/Representation Theory [math.RT]