Minuscule Coxeter Dressians

TL;DR

This paper introduces Coxeter Dressians, a class of tropical prevarieties related to Coxeter matroids, extending known results from type A to other Lie types, with computational implementations.

Contribution

It generalizes the concept of Dressians to Coxeter matroids across various Lie types and provides explicit computational methods using OSCAR.

Findings

Subdivisions induced by Coxeter Dressians are strong Coxeter matroidal.

Generalization of type A results to other Lie types.

Implementation of Coxeter Dressians computations in OSCAR.

Abstract

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.