Lookup NU author(s): Dr David Stewart
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. 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.
Author(s): Martin BMS, Stewart DI, Topley LW
Publication type: Article
Publication status: Published
Journal: Representation Theory
Online publication date: 16/09/2019
Acceptance date: 25/07/2019
Date deposited: 26/07/2019
ISSN (electronic): 1088-4165
Publisher: American Mathematical Society
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