τ-Functions, Birkhoff Factorizations and Difference Equations

Darlayne Addabbo, Maarten Bergvelt

Research output: Contribution to journalArticle

Abstract

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 Q -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 threecomponent fermionic Fock space leads to a new system of 4 difference equations.

Original languageEnglish (US)
Article number023
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume15
DOIs
StatePublished - Jan 1 2019

Keywords

  • Birkhoff factorizations
  • Integrable systems
  • Q- and t-systems
  • τ -functions

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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