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arXiv · hep-th/9311067

Additional Symmetries of Generalized Hierarchies

T. J. Hollowood·J. L. Miramontes·J. Sanchez Guillen
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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 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.

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T. J. Hollowood, J. L. Miramontes, J. Sanchez Guillen. 1993-11-11. Additional Symmetries of Generalized Hierarchies. https://doi.org/10.1088/0305-4470%2F27%2F13%2F036

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