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 Wn-gravitational ground ring spectra of these theories in terms of affine-SU(n) highest weights.