Dissimilarity maps on trees and the representation theory of SL m(ℂ)

Christopher Manon

doi:10.1007/s10801-010-0241-9

Dissimilarity maps on trees and the representation theory of SL _m(ℂ)

Christopher Manon

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We prove that m-dissimilarity vectors of weighted trees are points on the tropical Grassmannian, as conjecture by Cools in response to a question of Sturmfels and Pachter. We accomplish this by relating m-dissimilarity vectors to the representation theory of SL_m(ℂ).

Original language	English
Pages (from-to)	199-213
Number of pages	15
Journal	Journal of Algebraic Combinatorics
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s10801-010-0241-9
State	Published - Mar 2011

Bibliographical note

Funding Information:
This work was supported by the NSF fellowship DMS-0902710.

Funding

This work was supported by the NSF fellowship DMS-0902710.

Funders	Funder number
National Science Foundation Arctic Social Science Program	DMS-0902710
Directorate for Mathematical and Physical Sciences	0902710

Keywords

Representation theory
Tropical geometry

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s10801-010-0241-9

Cite this

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abstract = "We prove that m-dissimilarity vectors of weighted trees are points on the tropical Grassmannian, as conjecture by Cools in response to a question of Sturmfels and Pachter. We accomplish this by relating m-dissimilarity vectors to the representation theory of SLm(ℂ).",

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