Geodesic
Dissimilarity maps on trees and the representation theory of \(\mathrm{GL}_n(\mathbb{C})\)
Christopher Manon1
1George Mason University
The electronic journal of combinatorics, Tome 19 (2012) no. 3
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We revisit representation theory in type $A,$ used previously to establish that the dissimilarity vectors of phylogenetic trees are points on the tropical Grassmannian variety. We use a different version of this construction to show that the space of phylogenetic trees $K_n$ maps to the tropical varieties of every flag variety of $GL_n(\mathbb{C}).$ Using this map, we find a tropical function on the space of phylogenetic trees for each semistandard tableaux, and we show that the functions satisfy the tropicalized equations which cut out $GL_n(\mathbb{C})$ flag varieties.
DOI : 10.37236/2715
Classification : 05E10
Mots-clés : tropical geometry, flag variety, phylogenetic trees, branching

Christopher Manon  1

1 George Mason University 
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     title = {Dissimilarity maps on trees and the representation theory of {\(\mathrm{GL}_n(\mathbb{C})\)}},
     journal = {The electronic journal of combinatorics},
     year = {2012},
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     number = {3},
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Christopher Manon. Dissimilarity maps on trees and the representation theory of \(\mathrm{GL}_n(\mathbb{C})\). The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2715

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