Symmetries of the Classical Integrable Systems and 2-Dimensional Quantum Gravity: a ‘Map’

Abstract

We draw attention to the connections recently established by others between the classical integrable KdV and KP hierarchies in 1 + 1 and 2 + 1 dimensions respectively and the matrix models which relate to the partition functions of 2-dimensional (1 + 1 dimensional) quantum gravity. The symmetries of the classical KP hierarchy in 2 + 1 dimensions are fundamental to this connection.