Litterick, Alastair and Thomas, Adam (2025) Complete reducibility in bad characteristic. Algebra & Number Theory. (In Press)
Litterick, Alastair and Thomas, Adam (2025) Complete reducibility in bad characteristic. Algebra & Number Theory. (In Press)
Litterick, Alastair and Thomas, Adam (2025) Complete reducibility in bad characteristic. Algebra & Number Theory. (In Press)
Abstract
Let G be a simple algebraic group of exceptional type over an algebraically closed field of characteristic p > 0. This paper continues a long-standing effort to classify the connected reductive subgroups of G. Having previously completed the classification when p is sufficiently large, we focus here on the case that p is bad for G. We classify the connected reductive subgroups of G which are not G-completely reducible, whose simple components have rank at least 3. For each such subgroup X, we determine the action of X on the adjoint module L(G) and on a minimal non-trivial G-module, and the connected centraliser of X in G. As corollaries we obtain information on: subgroups which are maximal among connected reductive subgroups; products of commuting G-completely reducible subgroups; subgroups with trivial connected centraliser; and subgroups which act indecomposably on an adjoint or minimal module for G.
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 30 Mar 2026 15:16 |
| Last Modified: | 30 Mar 2026 15:17 |
| URI: | http://repository.essex.ac.uk/id/eprint/42354 |
Available files
Filename: badchar-ANT-post-referee.pdf