Michael Bate

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20222026

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math.RT2024

Geometric rigidity of simple modules for algebraic groups

Michael Bate, David I. Stewart

Let k be a field, let G be an affine algebraic k-group and V a finite-dimensional G-module. We say V is rigid if the socle series and radical series coincide for the action of G on…

math.GR2024

The subgroup structure of pseudo-reductive groups

Michael Bate, Ben Martin, Gerhard Röhrle +1

Let $k$ be a field. We investigate the relationship between subgroups of a pseudo-reductive $k$ -group $G$ and its maximal reductive quotient $G^{'}$ , with applications to the subgroup…

math.GR2024

On good $A_{1}$ subgroups, Springer maps, and overgroups of distinguished unipotent elements in reductive groups

Michael Bate, Sören Böhm, Benjamin Martin +1

Suppose $G$ is a simple algebraic group defined over an algebraically closed field of good characteristic $p$ . In 2018 Korhonen showed that if $H$ is a connected reductive subgroup…

math.RT2024

$G$ -complete reducibility and saturation

Michael Bate, Sören Böhm, Alastair Litterick +2

Let $H \subseteq G$ be connected reductive linear algebraic groups defined over an algebraically closed field of characteristic $p > 0$ . In our first main theorem we show that if a…

Geometric rigidity of simple modules for algebraic groups

The subgroup structure of pseudo-reductive groups

On good A1​ subgroups, Springer maps, and overgroups of distinguished unipotent elements in reductive groups

G-complete reducibility and saturation

On good $A_{1}$ subgroups, Springer maps, and overgroups of distinguished unipotent elements in reductive groups

$G$ -complete reducibility and saturation