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

Kaie Kubjas, Christopher Manon*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

Work of BuczyA"ska, WiA > niewski, Sturmfels and Xu, and the second author has linked the group-based phylogenetic statistical model associated with the group with the Wess-Zumino-Witten (WZW) model of conformal field theory associated to . In this article we explain how this connection can be generalized to establish a relationship between the phylogenetic statistical model for the cyclic group and the WZW model for the special linear group 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 phylogenetic statistical model.

Original languageEnglish
Pages (from-to)861-886
Number of pages26
JournalJOURNAL OF ALGEBRAIC COMBINATORICS
Volume40
Issue number3
DOIs
Publication statusPublished - Nov 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • Conformal blocks
  • Phylogenetics
  • Semigroup algebras
  • HONEYCOMB MODEL
  • MODULI SPACES
  • PRODUCTS
  • TREES
  • COEFFICIENTS
  • INVARIANTS
  • BUNDLES

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