1993/11/11 by T. J. Hollowood, J. L. Miramontes, J. Sanchez Guillen
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1088/0305-4470/27/13/036
published as J.Phys. A27 (1994) 4629-4644 · 24 pages, (macro included), CERN-TH.6998/93, US-FT-8/93, SWAT/93-92/10
arxiv created 1993/11/11 · arxiv updated 2016/09/06
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 rôle 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.