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The \(m-\)dissimilarity map and representation theory of \(SL_m\)
Preprint
2010-03-21
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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 \(SL_m.\)