Realization of the Space of Conformal Blocks in Lie Algebra Modules,

Using integrable irreducible representations of generalized twisted affine Lie algebra modules, we give a realization of the space of conformal blocks of conformal field theory on a stable algebraic curve. Many basic properties of the conformal blocks, such as finite dimensionality of the space, invariance of the conformal blocks under suitable formal neighborhood changes, and the property of “propagation of vacua” are discussed. Finally, a relative local 1-form around a fixed point of the order two automorphism of the curve is given.