nLab Y-system

Redirected from "T-system".
Literature

33## Overview

Y-system and T-system are two related classes of algebraic relations associated with affine Lie algebras and can be considered as encoding certain integrable systems. Y-system can be considered as a system of difference equation?s for a finite set of commuting variables Y iY_i, iIi\in I,

Y i(t+1)Y i(t1)= ji(Y j(t)+1) a ij Y_i(t+1)Y_i(t-1)=\prod_{j\neq i}\bigl(Y_j(t)+ 1\bigr)^{-a_{ij}}

The elements of the T-system satisfy discrete Hirota equations.

Literature

For reviews see

  • Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki, T-systems and Y-systems in integrable systems, J. Phys. A44 103001 (2011) doi; T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras, SIGMA 5 (2009), 108, 23 pages

Y-system has a remarkable connection to cluster algebras:

Y-systems are relevant for integrability phenomena in superstring theory and in relation to study of spectrum of N=4 SUSY Yang-Mills theory. See survey

  • Stijn J. van Tongeren, Integrability of the AdS 5×S 5AdS_5 \times S^5 superstring and its deformations, J. Phys. A: Math. Theor. 47 (2014) 433001 arXiv:1310.4854

On Q- and T-system

  • Philippe Di Francesco, Discrete integrable systems, positivity, and continued fraction rearrangements, Lett Math Phys 96 (2011) 299–324 doi
category: physics

Last revised on July 31, 2024 at 13:02:05. See the history of this page for a list of all contributions to it.