Michael Bate

collaborators

4 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.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.RT2025

$G$ -complete reducibility and saturation

Michael Bate, SÃ¶ren BÃ¶hm, 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.RT2025

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…

Clique complexes of groups and order sheaves

Homology of matching complexes and representations of symmetric groups

G-complete reducibility and saturation

Geometric rigidity of simple modules for algebraic groups

$G$ -complete reducibility and saturation