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

Benjamin Martin, David Stewart, Lewis Topley

Research output: Working paper

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Abstract

In 1971, Kac and Weisfeiler made two influential conjectures describing the dimensions of simple modules of a restricted Lie algebra $\mathfrak{g}$. The first predicts the maximal dimension of simple $\mathfrak{g}$-modules and in this paper we apply the Lefschetz principle and classical techniques from Lie theory to prove this conjecture for all restricted Lie subalgebras of $\mathfrak{gl}_n(k)$ whenever $k$ is an algebraically closed field of characteristic $p \gg n$. As a consequence we deduce that the conjecture holds for the the Lie algebra of a group scheme when specialised to an algebraically closed field of almost any characteristic.
Original languageEnglish
PublisherArXiv
Publication statusSubmitted - 30 Oct 2018

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Algebraically closed
Lie Algebra
Simple Module
Group Scheme
Subalgebra
Deduce
Predict
Module

Keywords

  • math.RT
  • math.RA

Cite this

A proof of the first Kac-Weisfeiler conjecture in large characteristics. / Martin, Benjamin; Stewart, David; Topley, Lewis.

ArXiv, 2018.

Research output: Working paper

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