The $m-$dissimilarity map and representation theory of $SL_m$

Details The $m-$dissimilarity map and representation theory of $SL_m$ The $m-$dissimilarity map and representation theory of $SL_m$

2010-03-21

arxiv.org/abs/1003.3970v2

Mathematics

Algebraic Geometry

11 pages, 8 figures

Scientific paper

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 $SL_m.$

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