Séminaire Lotharingien de Combinatoire, 95B.58 (2026), 12 pp.
Kieran Calvert, Aram Dermenjian, Alex Fink and Ben Smith
Quadratic Exchange Equations for Coxeter Matroids
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.
In this extended abstract we focus on type B, with all other types being handled in arXiv:2511.13498.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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