  The conformal non-compact $SL(2,R)/U(1)$ coset model in two dimensions has
been recently shown to embody a nonlinear $\hat{W}_\infty$ current algebra,
consisting of currents of spin $\geq 2$ including the energy-momentum tensor.
In this letter we explicitly construct an infinite set of commuting quantum
$\hat{W}_\infty$ charges in the model with $k=1$. These commuting quantum
charges generate a set of infinitely many compatible flows (quantum KP flows),
which maintain the nonlinear $\hat{W}_\infty$ current algebra invariant.
