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A proof of the first Kac-Weisfeiler conjecture in large characteristics

Lookup NU author(s): Dr David StewartORCiD

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by American Mathematical Society, 2019.

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Abstract

Abstract. In 1971, Kac and Weisfeiler made two influential conjectures describingthe dimensions of simple modules of a restricted Lie algebra g. The first predicts themaximal dimension of simple g-modules and in this paper we apply the Lefschetz Prin-ciple and classical techniques from Lie theory to prove this conjecture for all restrictedLie subalgebras of gl n pkq whenever k is an algebraically closed field of characteristicp " 0. As a consequence we deduce that the conjecture holds for the the Lie alge-bra of a group scheme when specialised to an algebraically closed field of almost anycharacteristic.

Publication metadata

Author(s): Martin BMS, Stewart DI, Topley LW

Publication type: Article

Publication status: Published

Journal: Representation Theory

Year: 2019

Volume: 23

Pages: 278-293

Online publication date: 16/09/2019

Acceptance date: 25/07/2019

Date deposited: 26/07/2019

ISSN (electronic): 1088-4165

Publisher: American Mathematical Society

URL: https://doi.org/10.1090/ert/529

DOI: 10.1090/ert/529

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