{"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/kazhdan-constants-for-chevalley-groups-over","title":"Kazhdan constants for Chevalley groups over the integers","arxiv_id":"2306.12358","date":"2023-06-21","proceeding":null,"authors":["Marek Kaluba","Dawid Kielak"],"abstract":"We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than $\\mathtt{A}_{n}$, these are the first explicit asymptotically sharp such bounds. The method relies on establishing a new connection between the structure of a root system grading a family of groups and the behaviour of the square of the Laplace operator in the family.","url_abs":"https://arxiv.org/abs/2306.12358v3","url_pdf":"https://arxiv.org/pdf/2306.12358v3.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":"kazhdan-constants-for-chevalley-groups-over","repo_url":"https://github.com/kalmarek/2306.12358","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"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}