{"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/the-generalized-linear-period","title":"The generalized linear period","arxiv_id":"2004.00447","date":"2020-04-01","proceeding":null,"authors":["Hengfei Lu"],"abstract":"Let $F$ be a non-archimedean local field of characteristic zero. We study the linear period problem for the pair $(G,H_{p,p+1})=(GL_{2p+1}(F), GL_{p}(F)\\times GL_{p+1}(F))$ and we prove that any bi-$(H_{p,p+1},\\mu)$-invariant generalized function on $G$ is invariant under the matrix transpose when \\mu is a good character. We also show that any $P\\cap H_{p,p+1}$-invariant linear functional on an $H_{p,p+1}$-distinguished irreducible smooth representation of $G$ is also $H_{p,p+1}$-invariant when F is nonarchimedean, where $P$ is a standard mirabolic subgroup of $G$ with last row vector $(0,\\cdots,0,1)$.","url_abs":"https://arxiv.org/abs/2004.00447v3","url_pdf":"https://arxiv.org/pdf/2004.00447v3.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":"the-generalized-linear-period","repo_url":"https://github.com/masonlvhf/Hengfei","is_official":0,"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}