%0 Journal Article %T On the Algebraic Structure of Gravitational Descendants in CP(n-1) Coset Models %A W. Lerche %A N. P. Warner %J Physics %D 1994 %I arXiv %R 10.1016/0370-2693(94)01440-N %X 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.. %U http://arxiv.org/abs/hep-th/9409069v1