Minuscule Coxeter Dressians
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917137019305984 |
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| author | Gross, Andreas Kuehn, Kevin Luber, Dante |
| author_facet | Gross, Andreas Kuehn, Kevin Luber, Dante |
| contents | In this extended abstract, we study special tropical prevarieties which we call Coxeter Dressians. They arise from equations capturing a generalization of valuated symmetric basis exchange for Coxeter matroids. In particular, we study subdivisions of the associated Coxeter matroid polytopes. We show that the subdivisions induced by points of the Coxeter Dressian consist of cells which are strong Coxeter matroidal. This generalizes well-known results in type $A$ to other Lie types. Finally, we implement explicit computations of Coxeter Dressians in OSCAR. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09703 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minuscule Coxeter Dressians Gross, Andreas Kuehn, Kevin Luber, Dante Combinatorics Algebraic Geometry Representation Theory 52B40, 20F55 (Primary), 14T15, 14M17 (Secondary) In this extended abstract, we study special tropical prevarieties which we call Coxeter Dressians. They arise from equations capturing a generalization of valuated symmetric basis exchange for Coxeter matroids. In particular, we study subdivisions of the associated Coxeter matroid polytopes. We show that the subdivisions induced by points of the Coxeter Dressian consist of cells which are strong Coxeter matroidal. This generalizes well-known results in type $A$ to other Lie types. Finally, we implement explicit computations of Coxeter Dressians in OSCAR. |
| title | Minuscule Coxeter Dressians |
| topic | Combinatorics Algebraic Geometry Representation Theory 52B40, 20F55 (Primary), 14T15, 14M17 (Secondary) |
| url | https://arxiv.org/abs/2512.09703 |