The parabolic exotic t-structure

TL;DR

This paper extends the exotic t-structure concept from full flag varieties to partial flag varieties for reductive groups, establishing new equivalences and conjecture analogues in geometric representation theory.

Contribution

It introduces a parabolic analogue of the exotic t-structure on cotangent bundles of partial flag varieties and proves a related equivalence, advancing understanding in geometric representation theory.

Findings

Established a parabolic analogue of the Arkhipov-Bezrukavnikov-Ginzburg equivalence.

Proved a graded Finkelberg-Mirkovic conjecture analogue for certain singular blocks.

Extended the application of exotic t-structures to partial flag varieties.

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.