Conformal blocks, Berenstein–Zelevinsky triangles, and group-based models

Kaie Kubjas, Christopher Manon

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Pages (from-to)861-886
Number of pages26
JournalJournal of Algebraic Combinatorics
Issue number3
StatePublished - Oct 2 2014

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media New York 2014.


  • Conformal blocks
  • Phylogenetics
  • Semigroup algebras

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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