1993/03/19 by Michael Freeman, M. D. Freeman, Freeman, M. D. +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Mathematical and Computational Methods #Numerical methods for differential equations #Polynomial and algebraic computation #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9303119
(Talk given at the 1992 Johns Hopkins meeting, Goteborg, Sweden), 22 pages, KCL-TH-93-1
arxiv created 1993/03/19 · arxiv updated 2009/11/30
We review our work on the relation between integrability and infinite-dimensional algebras. We first consider the question of what sets of commuting charges can be constructed from the current of a \sf U(1) Kac-Moody algebra. It emerges that there exists a set Sn of such charges for each positive integer n>1; the corresponding value of the central charge in the Feigin-Fuchs realization of the stress tensor is c=13-6n-6/n. The charges in each series can be written in terms of the generators of an exceptional \W-algebra. We show that the \W-algebras that arise in this way are symmetries of Liouville theory for special values of the coupling. We then exhibit a relationship between the \nls equation and the KP hierarchy. From this it follows that there is a relationship between the \nls equation and the algebra \Wi. These examples provide evidence for our conjecture that the phenomenon of integrability is intimately linked with properties of infinite dimensional algebras.