Orbits of maximal and submaximal dimension for Sylow $p$-subgroups of finite classical groups

[2608.27523] Orbits of maximal and submaximal dimension for Sylow $p$-subgroups of finite classical groups Skip to main content Search Submit Donate Log in Mathematics > Representation Theory arXiv:2608.27523 (math) [Submitted on 27 Aug 2026] Title: Orbits of maximal and submaximal dimension for Sylow $p$-subgroups of finite classical groups Authors: Mikhail Ignatev , Mikhail Venchakov View PDF HTML (experimental) Abstract: Let $U$ be a Sylow $p$-subgroup in a classical group over a finite field with $q$ elements of characteristic $p$ large enough. The coadjoint orbits of the group $U$ play the key role in the description of irreducible complex characters of $U$. In the paper, we provide a classification of such orbits of pre-maximal dimension for symplectic groups and orbits of maximal dimension for orthogonal groups. As a corollary, we compute the number of all orbits mentioned above. It turned out that each of these numbers is a polynomial in $q - 1$ with integer non-negative coefficients, which agrees with the Isaacs' conjecture. Comments: 12 pages Subjects: Representation Theory (math.RT) MSC classes: 20C15, 17B08, 20D15 Cite as: arXiv:2608.27523 [math.RT] (or arXiv:2608.27523v1 [math.RT] for this version) https://doi.org/10.48550/arXiv.2608.27523 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mikhail Venchakov [ view email ] [v1] Thu, 27 Aug 2026 13:15:50 UTC (20 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2026-08 Change to browse by: math 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) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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