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arXiv · 2309.14312

Chow Rings of Matroids as Permutation Representations

Robert Angarone·Anastasia Nathanson·Victor Reiner
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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 Poincaré duality and the Hard Lefschetz theorem. We lift these to statements about this permutation action, and suggest further conjectures in this vein.

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Robert Angarone, Anastasia Nathanson, Victor Reiner. 2024-11-04. Chow Rings of Matroids as Permutation Representations. https://arxiv.org/abs/2309.14312

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