The m−m-dissimilarity map and representation theory of SLmSL_m

preprint2010arXivOpen access

Abstract

We give another proof that mm-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 mm-dissimilarity vectors to the representation theory of SLm.SL_m.

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