Precise constraints on a $\tau$ function in 2D quantum gravity

Abstract

For an arbitrary $p$, propose a new and computable method which can determine the values of unknown constants in constraints on a tau function which satisfies both the p-reduced KP hierarchy and the sting equation. All the constants do not equal 0, unlike what people usually think of. With these values, obtain the precise algebra that the constraints compose. This algebra includes none of $\{t_{mp}\}$ and also includes the Virasoro algebra as a subalgebra.