  We identify the algebra of matrix elements of big projective modules in
category O with the regular functions on the big Bruhat cell of G. Analogous
extensions of the regular representations of the affine Lie and Virasoro
algebras yield vertex operator algebras, equipped with two commuting actions
with special values of the total central charge. In the generic case, we
identify the structure of these VOAs, compute their semi-infinite cohomology.
Its superalgebra structure encodes the fusion rules for the associated tensor
categories. Full details are provided for the affine sl(2) and Virasoro
algebras, and various generalizations and extensions are discussed.
