Dissimilarity maps on trees and the representation theory of GL _n(ℂ)

We revisit representation theory in type A; used previously to establish that the dissimilarity vectors of phylogenetic trees are points on the tropical Grassmannian variety. We use a different version of this construction to show that the space of phylogenetic trees K _n maps to the tropical varieties of every flag variety of GL _n(ℂ): Using this map, we find a tropical function on the space of phylogenetic trees for each semistandard tableaux, and we show that the functions satisfy the tropicalized equations which cut out GL _n(ℂ) flag varieties.