Anne Thomas

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math.GR2026

Visualizing conjugation in affine Coxeter groups

Amy Herron, Anne Thomas

Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric proper…

math.GR2025

The geometry of conjugation in Euclidean isometry groups

Elizabeth MiliÄeviÄ, Petra Schwer, Anne Thomas

We describe the geometry of conjugation within any split subgroup $H$ of the full isometry group $G$ of $n$ -dimensional Euclidean space. We prove that for any $h \in H$ , the conjug…

math.GR2025

The geometry of conjugation in affine Coxeter groups

Elizabeth MiliÄeviÄ, Petra Schwer, Anne Thomas

We develop new and precise geometric descriptions of the conjugacy class $[x]$ and coconjugation set $C (x, x^{'}) = {y \in W ∣ y x y^{- 1} = x^{'}}$ for all…