Dissimilarity maps on trees and the representation theory of GLn()
Abstract
We revisit the representation theory in type Aused 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 Kn maps to the tropical varieties of every flag variety of GLn(). Using this map, we interpret the tropicalization of the semistandard tableaux basis of an irreducible representation of GLn() as combinatorial invariants of phylogenetic trees.
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