Additional Symmetries of Generalized Hierarchies
Abstract
The non-isospectral symmetries of a general class of integrable hierarchies are found, generalizing the Galilean and scaling symmetries of the Korteweg--de Vries equation and its hierarchy. The symmetries arise in a very natural way from the semi-direct product structure of the Virasoro algebra and the affine Kac--Moody algebra underlying the construction of the hierarchy. In particular, the generators of the symmetries are shown to satisfy a subalgebra of the Virasoro algebra. When a tau-function formalism is available, the infinitesimal symmetries act directly on the tau-functions as moments of Virasoro currents. Some comments are made regarding the r\^ole of the non-isospectral symmetries and the form of the string equations in matrix-model formulations of quantum gravity in two-dimensions and related systems.
Keywords
Cite
@article{arxiv.hep-th/9311067,
title = {Additional Symmetries of Generalized Hierarchies},
author = {T. J. Hollowood and J. L. Miramontes and J. Sanchez Guillen},
journal= {arXiv preprint arXiv:hep-th/9311067},
year = {2016}
}
Comments
24 pages, (macro included), CERN-TH.6998/93, US-FT-8/93, SWAT/93-92/10