Integral exotic sheaves and the modular Lusztig-Vogan bijection
| Autor: | Achar, Pramod N., Hardesty, William, Riche, Simon |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let G be a reductive group over an algebraically closed field k of very good characteristic. The Lusztig-Vogan bijection is a bijection between the set of dominant weights for G and the set of irreducible G-equivariant vector bundles on nilpotent orbits, conjectured by Lusztig and Vogan independently, and constructed in full generality by Bezrukavnikov. In characteristic 0, this bijection 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 support varieties 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 made precise in the body of the paper) independent of the characteristic of k. This allows us to extend all of its known properties from the characteristic-0 setting to the general case. We also expect this result to be a step towards a proof of the Humphreys conjecture on support varieties of tilting modules for reductive groups in positive characteristic. Comment: 49 pages. v2: weakened the assumptions on G throughout the paper |
| Databáze: | arXiv |
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