Jordan decomposition, categorical traces and Deligne-Lusztig theory

[2501.04113] Jordan decomposition, categorical traces and Deligne-Lusztig theory Skip to main content Search Submit Donate Log in Mathematics > Representation Theory arXiv:2501.04113 (math) [Submitted on 7 Jan 2025 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Jordan decomposition, categorical traces and Deligne-Lusztig theory Authors: Arnaud Eteve View PDF HTML (experimental) Abstract: This paper is a continuation of the author's previous work. We use the categorical trace formalism to construct a categorical Jordan decomposition for representations of finite groups of Lie type. As a second application, we study the endomorphism algebra of the Gelfand-Graev representation and recover a result of Li and Shotton-Li. Comments: Second version has been significantly enhanced. Comments are welcome Subjects: Representation Theory (math.RT) ; Algebraic Geometry (math.AG) Report number: MPIM-Bonn-2025 Cite as: arXiv:2501.04113 [math.RT] (or arXiv:2501.04113v2 [math.RT] for this version) https://doi.org/10.48550/arXiv.2501.04113 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arnaud Eteve [ view email ] [v1] Tue, 7 Jan 2025 19:42:20 UTC (52 KB) [v2] Thu, 27 Aug 2026 07:37:27 UTC (96 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2025-01 Change to browse by: math math.AG 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)

Related documents

• Jordan decomposition, categorical traces and Deligne-Lusztig theory#677348
• Flip Combinatorial Invariance and Weyl groups#1014545
• Chevalley-Eilenberg cohomology of linearly reductive Lie algebras in the Verlinde category#1062977
• Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models#499107
• Parabolic conjugacy class in finite reductive groups and its additive analogue#1049786