Quantum cluster algebras and fusion products

Research output: Contribution to journalArticle

Abstract

Q-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They can also be viewed as mutations in certain cluster algebras, which have a natural quantum deformation. In this paper, we explain the relation in the simply laced case between the resulting quantum Q-systems and the graded tensor product of Feigin and Loktev. We prove the graded version of the M=N identities, and write expressions for these as noncommuting evaluated multiresidues of suitable products of solutions of the quantum Q-system. This leads to a simple reformulation of Feigin and Loktev's fusion coefficients as matrix elements in a representation of the quantum Q-system algebra.

Original languageEnglish (US)
Pages (from-to)2593-2642
Number of pages50
JournalInternational Mathematics Research Notices
Volume2014
Issue number10
DOIs
StatePublished - 2014

Fingerprint

Cluster Algebra
Quantum Algebra
Fusion
Quantum Affine Algebra
Recursion Relations
Reformulation
Tensor Product
Mutation
Restriction
Module
Algebra
Coefficient

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Quantum cluster algebras and fusion products. / Di Francesco, Philippe; Kedem, Rinat.

In: International Mathematics Research Notices, Vol. 2014, No. 10, 2014, p. 2593-2642.

Research output: Contribution to journalArticle

@article{3d254a70a52e479ea23d3611cf5c5ebf,
title = "Quantum cluster algebras and fusion products",
abstract = "Q-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They can also be viewed as mutations in certain cluster algebras, which have a natural quantum deformation. In this paper, we explain the relation in the simply laced case between the resulting quantum Q-systems and the graded tensor product of Feigin and Loktev. We prove the graded version of the M=N identities, and write expressions for these as noncommuting evaluated multiresidues of suitable products of solutions of the quantum Q-system. This leads to a simple reformulation of Feigin and Loktev's fusion coefficients as matrix elements in a representation of the quantum Q-system algebra.",
author = "{Di Francesco}, Philippe and Rinat Kedem",
year = "2014",
doi = "10.1093/imrn/rnt004",
language = "English (US)",
volume = "2014",
pages = "2593--2642",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "10",

}

TY - JOUR

T1 - Quantum cluster algebras and fusion products

AU - Di Francesco, Philippe

AU - Kedem, Rinat

PY - 2014

Y1 - 2014

N2 - Q-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They can also be viewed as mutations in certain cluster algebras, which have a natural quantum deformation. In this paper, we explain the relation in the simply laced case between the resulting quantum Q-systems and the graded tensor product of Feigin and Loktev. We prove the graded version of the M=N identities, and write expressions for these as noncommuting evaluated multiresidues of suitable products of solutions of the quantum Q-system. This leads to a simple reformulation of Feigin and Loktev's fusion coefficients as matrix elements in a representation of the quantum Q-system algebra.

AB - Q-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They can also be viewed as mutations in certain cluster algebras, which have a natural quantum deformation. In this paper, we explain the relation in the simply laced case between the resulting quantum Q-systems and the graded tensor product of Feigin and Loktev. We prove the graded version of the M=N identities, and write expressions for these as noncommuting evaluated multiresidues of suitable products of solutions of the quantum Q-system. This leads to a simple reformulation of Feigin and Loktev's fusion coefficients as matrix elements in a representation of the quantum Q-system algebra.

UR - http://www.scopus.com/inward/record.url?scp=84900812122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84900812122&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnt004

DO - 10.1093/imrn/rnt004

M3 - Article

AN - SCOPUS:84900812122

VL - 2014

SP - 2593

EP - 2642

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 10

ER -