On the BRST structure of W(3) gravity coupled to c=2 matter
P. Bouwknegt, J. McCarthy and K. Pilch
ADP-93-203/M17, USC-93-1, hep-th/9303164,
in Perspectives in Mathematical Physics, eds. R. Penner and S.T. Yau, (International Press, 1994) pp. 77-89, [Proceedings of the AMS Special Session on Geometry and Physics, USC, Los Angeles, November 5-6, 1992].

We present some explicit results on the structure of singular vectors in $c=2$ Verma modules of the $\cW_3$ algebra. Using the embedding patterns of those vectors we construct resolutions for the $c=2$ irreducible modules, and thus are able to compute some of the BRST cohomology of $\cW_3$ gravity coupled to $c=2$ matter. In particular, we determine the states in the ground ring of the theory.

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