The $m-$dissimilarity map and representation theory of $SL_m$
Christopher Manon
TL;DR
This paper provides a new proof linking m-dissimilarity vectors of weighted trees to the tropical Grassmannian through the lens of SL_m representation theory, confirming a conjecture and connecting combinatorics with algebraic geometry.
Contribution
It offers an alternative proof that m-dissimilarity vectors lie on the tropical Grassmannian by relating them to the representation theory of SL_m, expanding understanding of their geometric and algebraic properties.
Findings
m-dissimilarity vectors are points on the tropical Grassmannian
Established a connection between combinatorial tree metrics and algebraic geometry
Provided an alternative proof of a conjecture by Cools, Giraldo, Sturmfels, and Pachter
Abstract
We give another proof that -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 -dissimilarity vectors to the representation theory of
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