Abstract
Based on the Korteweg-de Vries (KdV) hierarchy formulation of non-perturbative 2-d quantum gravity, we investigate the symmetries of the system. Particularly, it is shown that the recently found Virasoro constraints are due to the non-isospectral symmetries of KdV hierarchy, which can be interpreted as SL(2, C) invariance and the independence of the moduli of the auxiliary infinite genus hyperelliptic Riemann surfaces which appear in the Krichever construction of soliton solutions.
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