Vertex-algebraic structure of representations of affine Lie algebras
Abstract: Vertex operator algebras and intertwining operators play a fundamental role in the representation theory of affine Lie algebras. In this talk we discuss vertex-algebraic structure of the principal subspaces of standard modules for certain untwisted and twisted affine Lie algebras. We obtain presentations of these subspaces and fermionic formulas for their characters. Part of this talk is based on joint work with Jim Lepowsky and Antun Milas.