Séminaire Lotharingien de Combinatoire, 91B.24 (2024), 12 pp.
Robert Angarone, Anastasia Nathanson and Victor Reiner
Chow Rings of Matroids as Permutation Representations
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.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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