The Solution Space of the

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-deened continuum limit in which the string equation has the simple form P; Q ? ] = 1, with P and Q ? 2 2 matrices of diierential operators. These conditions on V 1 and V 2 yield a simple system of rst order diierential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints L n (n 0), where L n annihilate the two modiied-KdV-functions whose product gives the partition function of the Unitary Matrix Model.