Ramification of weak Arthur packets for p-adic groups

[2404.03485] Ramification of weak Arthur packets for p-adic groups Skip to main content Search Submit Donate Log in Mathematics > Representation Theory arXiv:2404.03485 (math) [Submitted on 4 Apr 2024 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Ramification of weak Arthur packets for p-adic groups Authors: Maxim Gurevich , Emile Okada View PDF HTML (experimental) Abstract: Weak Arthur packets have long been instrumental in the study of the unitary dual and automorphic spectrum of reductive Lie groups, and were recently introduced in the p-adic setting by Ciubotaru - Mason-Brown - Okada. For split odd orthogonal and symplectic p-adic groups, we explicitly determine the decomposition of weak Arthur packets into Arthur packets that arise from endoscopic transfer. We establish a characterization of the Arthur packets that partake in such decompositions by means of ramification properties of their constituents. A notion of weak sphericity for an irreducible representation is introduced: The property of containing fixed vectors with respect to a (not necessarily hyperspecial) maximal compact subgroup. We show that this property determines the weak Arthur packets in a precise sense. As steps towards this description, we explore alignments between Langlands-type reciprocities for finite and p-adic groups, and their dependence on the geometry of the unipotent locus of the dual Langlands group. Weak sphericity is shown to match with Lusztig's canonical quotient spaces that feature in the geometric theory for Weyl group representations, while the fine composition of weak Arthur packets is found to be governed by the partition of the unipotent locus into special pieces. Comments: 80 pages Subjects: Representation Theory (math.RT) ; Number Theory (math.NT) Cite as: arXiv:2404.03485 [math.RT] (or arXiv:2404.03485v2 [math.RT] for this version) https://doi.org/10.48550/arXiv.2404.03485 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Maxim Gurevich [ view email ] [v1] Thu, 4 Apr 2024 14:39:11 UTC (96 KB) [v2] Tue, 25 Aug 2026 07:32:31 UTC (93 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2024-04 Change to browse by: math math.NT References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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