Mathematics > Representation Theory
arXiv:2512.19034 (math)
[Submitted on 22 Dec 2025 (v1), last revised 1 Jul 2026 (this version, v2)]
Abstract:Let $G$ be a classical group defined over the complex numbers with a Borel subgroup $B$. Choose a holomorphic involution of $G$ and let $K$ be its set of fixed points. The group $K$ acts on the flag variety $G/B$ with finitely many orbits and Brion has derived a general formula for the cohomology classes of the corresponding orbit closures as linear combinations of Schubert classes. This article provides a uniform description of the sets of Weyl group elements (which we refer to as Brion atoms) that index the terms in this formula. This builds on prior work addressing types A, B, and C. The main novelty of our results is a thorough treatment of type D. As one application, we introduce a notion of involution Schubert polynomials for all classical types and present several conjectures related to these objects.
Submission history
From: Eric Marberg [view email]
[v1]
Mon, 22 Dec 2025 05:12:36 UTC (66 KB)
[v2]
Wed, 1 Jul 2026 15:30:43 UTC (68 KB)
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Code, Data, Media
Code, Data and Media Associated with this Article
Demos
Demos
Related Papers
Recommenders and Search Tools
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.



























