RATIONAL DIFFERENTIAL FORMS ON THE LINE AND SINGULAR VECTORS IN VERMA MODULES OVER (sl)over-cap(2)

摘要

We construct a monomorphism of the De Rham complex of scalar multivalued meromorphic forms on the projective line, holomorphic on the complement to a finite set of points, to the chain complex of the Lie algebra of (sl) over cap (2)-valued algebraic functions on the same complement with coefficients in a tensor product of contragradient Verma modules over the affine Lie algebra (sl) over cap (2). We show that the existence of singular vectors in the Verma modules (the Malikov Feigin Fuchs singular vectors) is reflected in the new relations between the cohomology classes of logarithmic differential forms.