On completeness of local intertwining periods

[2503.11988] On completeness of local intertwining periods Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Representation Theory arXiv:2503.11988 (math) [Submitted on 15 Mar 2025 ( v1 ), last revised 10 Apr 2026 (this version, v2)] Title: On completeness of local intertwining periods Authors: Hengfei Lu , Nadir Matringe View a PDF of the paper titled On completeness of local intertwining periods, by Hengfei Lu and 1 other authors View PDF HTML (experimental) Abstract: In this paper we study the problem of explicitly describing the space of invariant linear forms on induced distinguished representations in terms of invariant linear forms on the inducing representation. More precisely, for certain tempered reductive symmetric pairs (G,H) over a local field of characteristic zero, which we call unimodular in this paper, we study under which condition on the inducing representation, the space of H-invariant linear forms on a parabolically induced representation of G is generated by regularized intertwining periods attached to admissible parabolic orbits in G{H, as defined in the work of Matringe--Offen--Yang. We conjecture that it is the case when the inducing representation is square-integrable. Under this assumption we actually conjecture that one can replace regularized by normalized intertwining periods. We then verify the conjecture on known examples, and prove it for various pairs where G has semi-simple split rank one. Comments: Revised version to appear in Journal of Functional Analysis Subjects: Representation Theory (math.RT) Cite as: arXiv:2503.11988 [math.RT] (or arXiv:2503.11988v2 [math.RT] for this version) https://doi.org/10.48550/arXiv.2503.11988 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nadir Matringe [ view email ] [v1] Sat, 15 Mar 2025 04:10:13 UTC (35 KB) [v2] Fri, 10 Apr 2026 05:32:13 UTC (36 KB) Full-text links: Access Paper: View a PDF of the paper titled On completeness of local intertwining periods, by Hengfei Lu and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2025-03 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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) Major funding support from

Related documents

• A Proof of the Hodge Conjecture Derived from One Semiregular Witness Axiom - A Conditional Proof, the Deletion Test of Its Clauses, and the Open Fermat Orbit at Degree Seventy Outside Aoki's Lattice#689092
• Wave Numbers: Discrete Sequence Algebras, Sieve Projectors, and Dynamical Geometry#1048977
• On the invariance of irregular Hodge numbers under crepant birational equivalences#821948
• Universal constructions in algebraic and locally covariant quantum field theory#498758
• Beiträge zur Kunde Ehst-, Liv- und Kurlands, Bd.16, H.1-6#190927