Abstract
We study the holomorphic structure of certain complex manifolds associated withW∞ algebras, namely, the flag manifoldsW∞/T∞ andW1+∞/T1+∞, and the spacesW∞/SL(∞),R) andW1+∞/GL(∞,R), whereT∞ andT1+∞ are the maximal tori inW∞ andW1+∞. We compute their Ricci curvature and show how the results are related to the anomaly-freedom conditions forW∞ andW1+∞. We discuss the relation of these manifolds with extensions of universal Teichmuller space.
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