Geodesic
Conformal blocks, Berenstein-Zelevinsky triangles, and group-based models
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 3, pp. 861-886.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Work of Buczyńska, Wiśniewski, Sturmfels and Xu, and the second author has linked the group-based phylogenetic statistical model associated with the group $\mathbb Z/2\mathbb Z$ with the Wess-Zumino-Witten (WZW) model of conformal field theory associated to $\mathrm{SL}_2(\mathbb C)$. In this article we explain how this connection can be generalized to establish a relationship between the phylogenetic statistical model for the cyclic group $\mathbb Z/m\mathbb Z$ and the WZW model for the special linear group $\mathrm{SL}_m(\mathbb C)$. We use this relationship to also show how a combinatorial device from representation theory, the Berenstein-Zelevinsky triangle, corresponds to elements in the affine semigroup algebra of the $\mathbb Z/3\mathbb Z$ phylogenetic statistical model.
Classification : 14H10, 14D06, 17B10, 20G05
Keywords: conformal blocks, phylogenetics, semigroup algebras 
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     title = {Conformal blocks, {Berenstein-Zelevinsky} triangles, and group-based models},
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Kubjas, Kaie; Manon, Christopher. Conformal blocks, Berenstein-Zelevinsky triangles, and group-based models. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 3, pp. 861-886. http://geodesic.mathdoc.fr/item/JAC_2014__40_3_a0/