Quadratic exchange equations for Coxeter matroids
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917148135260160 |
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| author | Calvert, Kieran Dermenjian, Aram Fink, Alex Smith, Ben |
| author_facet | Calvert, Kieran Dermenjian, Aram Fink, Alex Smith, Ben |
| contents | Tropicalisation (with trivial coefficients) is a process that turns a polynomial equation into a combinatorial predicate on subsets of the set of variables. We show that for each minuscule representation of a simple reductive group, there is a set of quadratic equations cutting out the orbit of the highest weight vector whose tropicalisation characterises the set of Coxeter matroids for that representation which satisfy the strong exchange property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic exchange equations for Coxeter matroids Calvert, Kieran Dermenjian, Aram Fink, Alex Smith, Ben Combinatorics Representation Theory 20F55, 52B40 (Primary) 14M17, 14T15 (Secondary) Tropicalisation (with trivial coefficients) is a process that turns a polynomial equation into a combinatorial predicate on subsets of the set of variables. We show that for each minuscule representation of a simple reductive group, there is a set of quadratic equations cutting out the orbit of the highest weight vector whose tropicalisation characterises the set of Coxeter matroids for that representation which satisfy the strong exchange property. |
| title | Quadratic exchange equations for Coxeter matroids |
| topic | Combinatorics Representation Theory 20F55, 52B40 (Primary) 14M17, 14T15 (Secondary) |
| url | https://arxiv.org/abs/2511.13498 |