The Saito determinant for extended affine Weyl discriminant strata

[2608.26817] The Saito determinant for extended affine Weyl discriminant strata Skip to main content Search Submit Donate Log in Mathematics > Representation Theory arXiv:2608.26817 (math) [Submitted on 27 Aug 2026] Title: The Saito determinant for extended affine Weyl discriminant strata Authors: Andrea Brini , Karoline van Gemst View PDF HTML (experimental) Abstract: We investigate the form of the Saito metric on quotients of the reflection representation of an extended affine Weyl group, restricted to an arbitrary stratum of its discriminant. We compute the Saito determinant for all strata and Dynkin types and show that it is divisible by a product of q-analogues of restricted roots for the associated hyperplane arrangement. Our results simultaneously generalise the factorisation in the Weyl denominator formula to higher codimension strata, and provide q-analogue refinements of results of Antoniou-Feigin-Strachan for Coxeter groups. Comments: 25 pages Subjects: Representation Theory (math.RT) ; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Differential Geometry (math.DG) Cite as: arXiv:2608.26817 [math.RT] (or arXiv:2608.26817v1 [math.RT] for this version) https://doi.org/10.48550/arXiv.2608.26817 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Andrea Brini [ view email ] [v1] Thu, 27 Aug 2026 08:53:50 UTC (91 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Ancillary-file links: Ancillary files ( details ) : ExceptionalSeriesHighCodim.NB Current browse context: math.RT < prev | next > new | recent | 2026-08 Change to browse by: hep-th math math-ph math.AG math.DG math.MP References & Citations INSPIRE HEP 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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