Complete reducibility in bad characteristic
Abstract
Let be a simple algebraic group of exceptional type over an algebraically closed field of characteristic . This paper continues a long-standing effort to classify the connected reductive subgroups of . Having previously completed the classification when is sufficiently large, we focus here on the case that is bad for . We classify the connected reductive subgroups of which are not -completely reducible, whose simple components have rank at least . For each such subgroup , we determine the action of on the adjoint module and on a minimal non-trivial -module, and the connected centraliser of in . As corollaries we obtain information on: subgroups which are maximal among connected reductive subgroups; products of commuting -completely reducible subgroups; subgroups with trivial connected centraliser; and subgroups which act indecomposably on an adjoint or minimal module for .
Cite
@article{arxiv.2304.08388,
title = {Complete reducibility in bad characteristic},
author = {Alastair J. Litterick and Adam R. Thomas},
journal= {arXiv preprint arXiv:2304.08388},
year = {2023}
}
Comments
41 pages, comments welcome