{"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/multiplicity-one-for-the-pair-gl-n-d-gl-n-e","title":"Multiplicity one for the pair (GL(n,D),GL(n,E))","arxiv_id":"2105.10855","date":"2021-05-23","proceeding":null,"authors":["Hengfei Lu"],"abstract":"Let F be a local field of characteristic zero. Let D be a quaternion algebra over F. Let E be a quadratic field extension of F. Let {\\mu} be a character of GL(1,E). We study the distinction problem for the pair (GL(n,D), GL(n,E)) and we prove that any bi-(GL(n,E), {\\mu})-equivariant tempered generalized function on GL(n,D) is invariant with respect to an anti-involution. Then it implies that dimHom({\\pi},{\\mu}) is at most 1 by the generalized Gelfand-Kazhdan criterion. Thus we give a new proof to the fact that (GL(2n,F),GL(n,E)) is a Gelfand pair when {\\mu} is trivial and D splits.","url_abs":"https://arxiv.org/abs/2105.10855v1","url_pdf":"https://arxiv.org/pdf/2105.10855v1.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":"multiplicity-one-for-the-pair-gl-n-d-gl-n-e","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":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}