Michael Bate

activity

20222026

collaborators

7 papers

math.GR2026

Clique complexes of groups and order sheaves

Michael Bate, Brent Everitt, Sam Ford

We study the clique complex $X_{G}$ of a finite group: a simplicial complex whose faces are in one-to-one correspondence with the elements of the group, and arise via a decomposition…

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…

math.GR2023

Homology of matching complexes and representations of symmetric groups

Michael Bate, Brent Everitt, Sam Ford +1

We compute the homology of the matching complex $M (Γ)$ , where $Γ$ is the complete hypergraph on $n \geq 2$ vertices, and analyse the $S_{n}$ -representations carried by this homology.…

math.GR2022

A construction of pseudo-reductive groups with non-reduced root system

Michael Bate, Gerhard Röhrle, Damian Sercombe +1

We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $B C_{n}$ ; these exist only in cha…