ON THE ALGEBRAIC STRUCTURE OF GRAVITATIONAL DESCENDANTS IN CP(N-1) COSET MODELS

We investigate how specific free-field realizations of twisted N = 2 s upersymmetric coset models give rise to natural extensions of the ''ma tter'' Hilbert spaces in such a manner as to incorporate the various g ravitational excitations. In particular, we show that adopting a parti cular screening prescription is equivalent to imposing the requisite e quivariance condition on cohomology. We find a simple algebraic charac terization of the W-n-gravitational ground ring spectra of these theor ies in terms of affine-SU(n) highest weights.