Elementary divisors of the Cartan matrix for partial characters

[2608.27570] Elementary divisors of the Cartan matrix for partial characters Skip to main content Search Submit Donate Log in Mathematics > Group Theory arXiv:2608.27570 (math) [Submitted on 27 Aug 2026] Title: Elementary divisors of the Cartan matrix for partial characters Authors: Kaveh Dastouri , Taro Sakurai View PDF HTML (experimental) Abstract: Let $\pi$ be a set of primes and let $G$ be a finite $\pi$-separable group. We prove that the Cartan matrix $C$ for the $\pi$-partial characters of $G$ is equivalent over the integers to a matrix $\operatorname{diag}(|\mathbf{C}_G(x)|_{\pi'})$, where $x$ runs over a set of representatives of the $\pi$-classes of $G$. In particular, we prove that $\det C = \prod |\mathbf{C}_G(x)|_{\pi'}.$ Comments: 7 pages, 2 tables Subjects: Group Theory (math.GR) ; Representation Theory (math.RT) MSC classes: 20C15 (Primary) 20C20 (Secondary) Cite as: arXiv:2608.27570 [math.GR] (or arXiv:2608.27570v1 [math.GR] for this version) https://doi.org/10.48550/arXiv.2608.27570 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Taro Sakurai [ view email ] [v1] Thu, 27 Aug 2026 18:00:30 UTC (8 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2026-08 Change to browse by: math math.RT 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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