Dissimilarity maps on trees and the representation theory of SL m(\Bbb C)
Christopher Manon
DOI: 10.1007/s10801-010-0241-9
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 (\Bbb C).
Pages: 199–213
Keywords: keywords tropical geometry; representation theory
Full Text: PDF
References
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2. Bocci, C., Cools, F.: A tropical interpretation of m-dissimilarity maps. Appl. Math. Comput. 212(2), 349-356 (2009)
3. Cools, F.: On the relation between weighted trees and tropical Grassmannians. J. Symb. Comput. 44(8), 1079-1086 (2009)
4. Dolgachev, I.: Lectures on Invariant Theory. London Mathematical Society Lecture Note Series, vol.
296. Cambridge University Press, Cambridge (2003)
5. Fulton, W., Harris, J.: Representation Theory. Graduate Texts in Mathematics, vol.
129. Springer, Berlin (1991)
6. Giraldo, B.I.: Dissimilarity vectors of trees are contained in the tropical Grassmannian. Electron. J. Comb. 17(1) (2010)
7. Grosshans, F.D.: Algebraic Homogeneous Spaces and Invariant Theory. Springer Lecture Notes, vol.
1673. Springer, Berlin (1997)
8. Manon, C.: The algebra of conformal blocks.
9. Manon, C.: Graded valuations and tropical geometry.
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