We revisit the 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 interpret the tropicalization of the semistandard tableaux basis of an irreducible representation of $GL_n(\C)$ as combinatorial invariants of phylogenetic trees.
The connection between representation theory and Schubert calculus
Report on "Geometry and representation theory of tensors for computer science, statistics and other areas."
The $m-$dissimilarity map and representation theory of $SL_m$
![QR code for arXiv:1107.3668 [math.AG]](http://oss.arxitics.com/images/favicon.svg)