Visualizing conjugation in affine Coxeter groups

[2605.29337] Visualizing conjugation in affine Coxeter groups Skip to main content Search Submit Donate Log in Mathematics > Group Theory arXiv:2605.29337 (math) [Submitted on 28 May 2026 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: Visualizing conjugation in affine Coxeter groups Authors: Amy Herron , Anne Thomas View PDF HTML (experimental) 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 Milićević, 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. Comments: 13 pages, 5 figures, all in color. Version 2: added discussion of components of conjugacy classes, revised color treatment for coconjugation sets, expanded discussion of color choices for our app, added discussion of connections to the arts Subjects: Group Theory (math.GR) Cite as: arXiv:2605.29337 [math.GR] (or arXiv:2605.29337v2 [math.GR] for this version) https://doi.org/10.48550/arXiv.2605.29337 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Anne Thomas [ view email ] [v1] Thu, 28 May 2026 04:17:25 UTC (4,535 KB) [v2] Wed, 26 Aug 2026 22:49:52 UTC (4,571 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2026-05 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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