Michael Bate

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20242026

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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.GR2025

Homology of matching complexes and representations of symmetric groups

Michael Bate, Brent Everitt, Sam Ford +1

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

math.GR2024

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

Michael Bate, SÃ¶ren BÃ¶hm, 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.GR2024

The subgroup structure of pseudo-reductive groups

Michael Bate, Ben Martin, Gerhard RÃ¶hrle +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…

Clique complexes of groups and order sheaves

Homology of matching complexes and representations of symmetric groups

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

The subgroup structure of pseudo-reductive groups

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