  We construct a countable number of differential operators $\hat{L}_n$ that
annihilate a generating function for intersection numbers of $\kappa$ classes
on $\Moduli_g$ (the $\kappa$-potential). This produces recursions among
intersection numbers of $\kappa$ classes which determine all such numbers from
a single initial condition. The starting point of the work is a combinatorial
formula relating intersecion numbers of $\psi$ and $\kappa$ classes. Such a
formula produces an exponential differential operator acting on the
Gromov-Witten potential to produce the $\kappa$-potential; after restricting to
a hyperplane, we have an explicit change of variables relating the two
generating functions, and we conjugate the "classical" Virasoro operators to
obtain the operators $\hat{L}_n$.
