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arXiv · 2605.29337

Visualizing conjugation in affine Coxeter groups

Amy Herron·Anne Thomas
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Abstract

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 properties. Using recent structural results of Mili\'cevi\'c, Schwer and the second author, we develop an app to visualize conjugation in affine Coxeter groups in dimensions 2 and 3. We explain the mathematics underlying this visualization, and connect its visual features to the arts.

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Amy Herron, Anne Thomas. 2026-05-28. Visualizing conjugation in affine Coxeter groups. https://arxiv.org/abs/2605.29337

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