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Let G be a reductive group over an algebraically closed field k of very goodcharacteristic. The Lusztig-Vogan bijection is a bijection between the set ofdominant weights for G and the set of irreducible G-equivariant vector bundleson nilpotent orbits, conjectured by Lusztig and Vogan independently, andconstructed in full generality by Bezrukavnikov. In characteristic 0, thisbijection is related to the theory of 2-sided cells in the affine Weyl group,and plays a key role in the proof of the Humphreys conjecture on supportvarieties of tilting modules for quantum groups at a root of unity.  In this paper, we prove that the Lusztig-Vogan bijection is (in a way madeprecise in the body of the paper) independent of the characteristic of k. Thisallows us to extend all of its known properties from the characteristic-0setting to the general case. We also expect this result to be a step towards aproof of the Humphreys conjecture on support varieties of tilting modules forreductive groups in positive characteristic.

Integral exotic sheaves and the modular Lusztig-Vogan bijection