Howe duality over finite fields I: The two stable ranges

[2412.15346] Howe duality over finite fields I: The two stable ranges Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Representation Theory arXiv:2412.15346 (math) [Submitted on 19 Dec 2024 ( v1 ), last revised 11 Apr 2026 (this version, v3)] Title: Howe duality over finite fields I: The two stable ranges Authors: Sophie Kriz View a PDF of the paper titled Howe duality over finite fields I: The two stable ranges, by Sophie Kriz View PDF HTML (experimental) Abstract: This is the first in a series of papers on type I Howe duality for finite fields, concerning the restriction of an oscillator representation of the symplectic group to a product of a symplectic and an orthogonal group. The goal of the series is describing this restriction completely explicitly. Applications (described in the third paper of the series) include demonstrating that the tensor pairs previously calculated by S.-Y. Pan as occuring with non-zero multiplicity occur with multiplicity 1, proving the type C case of the Gurevich-Howe rank conjecture, and giving a recursive formula for the characters of cuspidal unipotent representations. In this first paper, we construct the correspondence in the two so called stable ranges, where the rank of one of the factors is large enough with respect to the other. Comments: Some minor corrections, standardized notation, historical context, and references added Subjects: Representation Theory (math.RT) MSC classes: 11F27, 20C33, 20G40 Cite as: arXiv:2412.15346 [math.RT] (or arXiv:2412.15346v3 [math.RT] for this version) https://doi.org/10.48550/arXiv.2412.15346 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sophie Kriz [ view email ] [v1] Thu, 19 Dec 2024 19:23:14 UTC (29 KB) [v2] Sat, 28 Jun 2025 19:02:44 UTC (32 KB) [v3] Sat, 11 Apr 2026 20:51:20 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled Howe duality over finite fields I: The two stable ranges, by Sophie Kriz View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2024-12 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

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