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• W3195219690 startingPage "108024" @default.
• W3195219690 abstract "Let G be connected reductive algebraic group defined over an algebraically closed field of characteristic p>0 and suppose that p is a good prime for the root system of G, the derived subgroup of G is simply connected and the Lie algebra g=Lie(G) admits a non-degenerate (AdG)-invariant symmetric bilinear form. Given a linear function χ on g we denote by Uχ(g) the reduced enveloping algebra of g associated with χ. By the Kac–Weisfeiler conjecture (now a theorem), any irreducible Uχ(g)-module has dimension divisible by pd(χ) where 2d(χ) is the dimension of the coadjoint G-orbit containing χ. In this paper we give a positive answer to the natural question raised in the 1990s by Kac, Humphreys and the first-named author and show that any algebra Uχ(g) admits a module of dimension pd(χ)." @default.
• W3195219690 created "2021-08-30" @default.
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• W3195219690 date "2021-12-01" @default.
• W3195219690 modified "2023-10-18" @default.
• W3195219690 title "Modular representations of Lie algebras of reductive groups and Humphreys' conjecture" @default.
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• W3195219690 doi "https://doi.org/10.1016/j.aim.2021.108024" @default.
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