Chow rings of matroids as permutation representations

Robert Angarone; Anastasia Nathanson; Victor Reiner

doi:10.1112/jlms.70039

Chow rings of matroids as permutation representations

Robert Angarone, Anastasia Nathanson, Victor Reiner

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Given a matroid with a symmetry group, we study the induced group action on the Chow ring of the matroid with respect to symmetric building sets. 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.

Original language	English (US)
Article number	e70039
Journal	Journal of the London Mathematical Society
Volume	111
Issue number	1
DOIs	https://doi.org/10.1112/jlms.70039
State	Published - Jan 2025

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© 2024 The Author(s). Journal of the London Mathematical Society is copyright © London Mathematical Society.

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Chow rings of matroids as permutation representations

Abstract

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