Chow Rings of Matroids as Permutation Representations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915004729524224 |
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| author | Angarone, Robert Nathanson, Anastasia Reiner, Victor |
| author_facet | Angarone, Robert Nathanson, Anastasia Reiner, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14312 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Chow Rings of Matroids as Permutation Representations Angarone, Robert Nathanson, Anastasia Reiner, Victor Combinatorics 05B35, 05E18, 05E14 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. |
| title | Chow Rings of Matroids as Permutation Representations |
| topic | Combinatorics 05B35, 05E18, 05E14 |
| url | https://arxiv.org/abs/2309.14312 |