{"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/parabolically-induced-representations-of-p","title":"Parabolically induced representations of p-adic $G_2$ distinguished by $SO_4$, I","arxiv_id":"2203.05713","date":"2022-03-11","proceeding":null,"authors":["Sarah Dijols"],"abstract":"We consider the parabolically induced representations of the symmetric space $SO_4\\backslash G_2$ over a p-adic field using the geometric lemma when the inducing parabolic is $P_{\\beta}$. Using an explicit description of the embedding of $G_2$ in $GL_8$, we characterize precisely the induced representations which are $(SO_4, \\chi)$-distinguished, given a certain type of involutions is chosen.","url_abs":"https://arxiv.org/abs/2203.05713v4","url_pdf":"https://arxiv.org/pdf/2203.05713v4.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":"parabolically-induced-representations-of-p","repo_url":"https://github.com/sarahdijols/g2so4","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}