τ-Functions, Birkhoff Factorizations and Difference Equations

Q-systems and T-systems are systems of integrable difference equations that have recently attracted much attention and have wide applications in representation theory and statistical mechanics. We show that certain τ-functions, given as matrix elements of the action of the loop group of GL₂ on two-c...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2019
Main Authors: Addabbo, D., Bergvelt, M.
Format: Article
Language:English
Published: Інститут математики НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210052
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:τ-Functions, Birkhoff Factorizations and Difference Equations / D. Addabbo, M. Bergvelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862555453024632832
author Addabbo, D.
Bergvelt, M.
author_facet Addabbo, D.
Bergvelt, M.
citation_txt τ-Functions, Birkhoff Factorizations and Difference Equations / D. Addabbo, M. Bergvelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description Q-systems and T-systems are systems of integrable difference equations that have recently attracted much attention and have wide applications in representation theory and statistical mechanics. We show that certain τ-functions, given as matrix elements of the action of the loop group of GL₂ on two-component fermionic Fock space, give solutions of a Q-system. An obvious generalization using the loop group of GL₃ acting on three-component fermionic Fock space leads to a new system of 4 difference equations.
first_indexed 2025-12-07T21:24:12Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-210052
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T21:24:12Z
publishDate 2019
publisher Інститут математики НАН України
record_format dspace
spelling Addabbo, D.
Bergvelt, M.
2025-12-02T09:28:44Z
2019
τ-Functions, Birkhoff Factorizations and Difference Equations / D. Addabbo, M. Bergvelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 17B80
arXiv: 1605.00192
https://nasplib.isofts.kiev.ua/handle/123456789/210052
https://doi.org/10.3842/SIGMA.2019.023
Q-systems and T-systems are systems of integrable difference equations that have recently attracted much attention and have wide applications in representation theory and statistical mechanics. We show that certain τ-functions, given as matrix elements of the action of the loop group of GL₂ on two-component fermionic Fock space, give solutions of a Q-system. An obvious generalization using the loop group of GL₃ acting on three-component fermionic Fock space leads to a new system of 4 difference equations.
The authors gratefully acknowledge travel support from the Simons Foundation, Collaboration Grant 245048. Addabbo expresses thanks for support from Dr. Lois M. Lackner Mathematics Fellowships, the University of Illinois Research Board, and the Associate Alumnae of Douglass College. The authors also thank Philippe Di Francesco and Rinat Kedem for helpful conversations, and anonymous referees for many helpful comments.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
τ-Functions, Birkhoff Factorizations and Difference Equations
Article
published earlier
spellingShingle τ-Functions, Birkhoff Factorizations and Difference Equations
Addabbo, D.
Bergvelt, M.
title τ-Functions, Birkhoff Factorizations and Difference Equations
title_full τ-Functions, Birkhoff Factorizations and Difference Equations
title_fullStr τ-Functions, Birkhoff Factorizations and Difference Equations
title_full_unstemmed τ-Functions, Birkhoff Factorizations and Difference Equations
title_short τ-Functions, Birkhoff Factorizations and Difference Equations
title_sort τ-functions, birkhoff factorizations and difference equations
url https://nasplib.isofts.kiev.ua/handle/123456789/210052
work_keys_str_mv AT addabbod τfunctionsbirkhofffactorizationsanddifferenceequations
AT bergveltm τfunctionsbirkhofffactorizationsanddifferenceequations