Chow Rings of Matroids as Permutation Representations
Combinatorics
2024-11-06 v5
Abstract
Given a matroid and a group of its matroid automorphisms, we study the induced group action on the Chow ring of the matroid. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincar\'e duality and the Hard Lefschetz theorem. We lift these to statements about this permutation action, and suggest further conjectures in this vein.
Keywords
Cite
@article{arxiv.2309.14312,
title = {Chow Rings of Matroids as Permutation Representations},
author = {Robert Angarone and Anastasia Nathanson and Victor Reiner},
journal= {arXiv preprint arXiv:2309.14312},
year = {2024}
}
Comments
Version to appear in J. Lond. Math. Soc