The $m-$dissimilarity map and representation theory of $S{L}_m$

Abstract

We give another proof that $m$-dissimilarity vectors of weighted trees are points on the tropical Grassmanian, as conjectured by Cools, and proved by Giraldo in response to a question of Sturmfels and Pachter. We accomplish this by relating $m$-dissimilarity vectors to the representation theory of $S{L}_m.$

11 pages, 8 figures

References in corpus (2)

• Toric degenerations of spherical varieties
• Toric Degenerations and tropical geometry of branching algebras

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• On dissimilarity vectors of (not necessarily positive) weighted trees
• Tropical Grassmannian and Tropical Linear Varieties from phylogenetic trees