{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/good-position-braid-representatives-and","title":"Good position braid representatives and transversal slices of unipotent orbits","arxiv_id":"2310.12750","date":"2023-10-19","proceeding":null,"authors":["Chengze Duan"],"abstract":"Let G be a connected reductive group over an algebraically closed field and W be its Weyl group. Steinberg constructed a transversal slice of the regular unipotent orbit in G. This construction was generalized to n was generalized to unipotent orbits associated to any elliptic conjugacy classes of W by He and Lusztig via good minimal length elements. In this paper, we construct transversal slices for all unipotent orbits using the good elements in the associated braid monoid of W. As an application, we reformulate the dimension formula of affine Springer fibers using these good elements.","url_abs":"https://arxiv.org/abs/2310.12750v5","url_pdf":"https://arxiv.org/pdf/2310.12750v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"good-position-braid-representatives-and","repo_url":"https://github.com/cduan2024/gpbraid","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}