{"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/on-the-intersection-of-local-arthur-packets","title":"On the intersection of local Arthur packets for classical groups and applications","arxiv_id":"2201.10539","date":"2022-01-25","proceeding":null,"authors":["Alexander Hazeltine","Baiying Liu","Chi-Heng Lo"],"abstract":"In this paper, for symplectic and split odd special orthogonal groups, we develop an account of theory on the intersection problem of local Arthur packets. Specifically, following Atobe's reformulation on M{\\oe}glin's construction of local Arthur packets, we give a complete set of operators on the construction data, based on which, we provide algorithms and Sage codes to determine whether a given representation is of Arthur type. Furthermore, for any representation $\\pi$ of Arthur type, we give a precise formula for the set $$ \\Psi(\\pi)=\\{ \\text{local Arthur parameter }\\psi \\ | \\ \\text{the local Arthur packet } \\Pi_{\\psi} \\text{ contains } \\pi\\}.$$ Our results have many applications, including the precise counting of tempered representations in any local Arthur packet, specifying and characterizing \"the\" local Arthur parameter in $\\Psi(\\pi)$ for $\\pi$, especially when $\\pi$ belongs to several local Arthur packets but does not belong to any local $L$-packet of Arthur type.","url_abs":"https://arxiv.org/abs/2201.10539v3","url_pdf":"https://arxiv.org/pdf/2201.10539v3.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":"on-the-intersection-of-local-arthur-packets","repo_url":"https://github.com/chihenglo/intersection-of-local-arthur-packets","is_official":1,"mentioned_in_paper":1,"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}