On the Algebraic Structure of Gravitational Descendants in CP(n-1) Coset Models

We investigate how specific free-field realizations of twisted N=2 supersymmetric coset models give rise to natural extensions of the ``matter'' Hilbert spaces in such a manner as to incorporate the various gravitational excitations. In particular, we show that adopting a particular screening prescription is equivalent to imposing the requisite equivariance condition on cohomology. We find a simple algebraic characterization of the $W_n$-gravitational ground ring spectra of these theories in terms of affine-$SU(n)$ highest weights..