부산대학교 도서관

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.
Comment: Added missing stabilizer hypothesis (7) needed in the statement and proof of Theorem 1.1. The authors thank R. Pagaria for pointing out the issue