Irreducible representations of Lie algebras of reductive groups and the Kac-Weisfeiler conjecture |
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Authors: | Alexander Premet |
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Affiliation: | (1) Department of Mathematics, University of California, 92521 Riverside, CA, USA;(2) Present address: Department of Mathematics, University of Manchester, Oxford Road, M13 9PL Manchester, UK |
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Abstract: | Letg be the Lie algebra of a connected reductive groupG over an algebraically closed field of characteristicp>0. Suppose thatG(1) is simply connected andp is good for the root system ofG. Ifp=2, suppose in addition thatg admits a nondegenerateG-invariant trace form. LetV be an irreducible and faithfulg-module withp-character g*. It is proved in the paper that dimV is divisible byp1/2dim() where () stands for the orbit of under the coadjoint action ofG.Oblatum 14-III-1994 & 17-XI-1994 |
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