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

Kaie Kubjas; Christopher Manon

doi:10.1007/s10801-014-0511-z

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

Kaie Kubjas, Christopher Manon^*

^*Corresponding author for this work

George Mason University

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	861-886
Number of pages	26
Journal	JOURNAL OF ALGEBRAIC COMBINATORICS
Volume	40
Issue number	3
DOIs	https://doi.org/10.1007/s10801-014-0511-z
Publication status	Published - Nov 2014
MoE publication type	A1 Journal article-refereed

Keywords

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

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title = "Conformal blocks, Berenstein-Zelevinsky triangles, and group-based models",

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.",

keywords = "Conformal blocks, Phylogenetics, Semigroup algebras, HONEYCOMB MODEL, MODULI SPACES, PRODUCTS, TREES, COEFFICIENTS, INVARIANTS, BUNDLES",

author = "Kaie Kubjas and Christopher Manon",

year = "2014",

month = nov,

doi = "10.1007/s10801-014-0511-z",

language = "English",

volume = "40",

pages = "861--886",

journal = "JOURNAL OF ALGEBRAIC COMBINATORICS",

issn = "0925-9899",

publisher = "Springer",

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T1 - Conformal blocks, Berenstein-Zelevinsky triangles, and group-based models

AU - Kubjas, Kaie

AU - Manon, Christopher

PY - 2014/11

Y1 - 2014/11

N2 - 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.

AB - 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.

KW - Conformal blocks

KW - Phylogenetics

KW - Semigroup algebras

KW - HONEYCOMB MODEL

KW - MODULI SPACES

KW - PRODUCTS

KW - TREES

KW - COEFFICIENTS

KW - INVARIANTS

KW - BUNDLES

U2 - 10.1007/s10801-014-0511-z

DO - 10.1007/s10801-014-0511-z

M3 - Article

SN - 0925-9899

VL - 40

SP - 861

EP - 886

JO - JOURNAL OF ALGEBRAIC COMBINATORICS

JF - JOURNAL OF ALGEBRAIC COMBINATORICS

IS - 3

ER -

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

Abstract

Keywords

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