Quadratic exchange equations for Coxeter matroids
Combinatorics
2025-12-17 v2 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2511.13498,
title = {Quadratic exchange equations for Coxeter matroids},
author = {Kieran Calvert and Aram Dermenjian and Alex Fink and Ben Smith},
journal= {arXiv preprint arXiv:2511.13498},
year = {2025}
}
Comments
49 pages, 7 figures. Added Remark 4.12, a discussion of type B and D equations derived in the literature. Moved proof of Theorem 4.8 to appendix