Petra Schwer

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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

Conjugator length of locally compact groups of Euclidean isometries

Yuri Santos Rego, Petra Schwer

We consider locally compact subgroups $H$ of the full isometry group $\Isom(\E^n)$ of Euclidean $n$ -space which respect the splitting into an orthogonal and a translation subgroup.…

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…