Work of Buczyńska, Wiśniewski, Sturmfels and Xu, and the second author has linked the group-based phylogenetic statistical model associated with the group ℤ/2ℤ with the Wess–Zumino–Witten (WZW) model of conformal field theory associated to SL2(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 ℤ/mℤ and the WZW model for the special linear group SLm(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 ℤ/3ℤ phylogenetic statistical model.
|Number of pages||26|
|Journal||Journal of Algebraic Combinatorics|
|State||Published - Oct 2 2014|
Bibliographical notePublisher Copyright:
© Springer Science+Business Media New York 2014.
- Conformal blocks
- Semigroup algebras
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics