Annihilating Fields of Standard Modules for Affine Lie Algebras

Abstract

Given an affine Kac-Moody Lie algebra $\tilde{\mathfrak{g}}[\sigma ]$ of arbitrary type, we determine certain minimal sets of annihilating fields of standard $\tilde{\mathfrak{g}}[\sigma ]$-modules. We then use these sets in order to obtain a characterization of standard $\tilde{\mathfrak{g}}[\sigma ]$-modules in terms of irreducible loop $\tilde{\mathfrak{g}}[\sigma ]$-modules, which proves to be a useful tool for combinatorial constructions of bases for standard $\tilde{\mathfrak{g}}[\sigma ]$-modules.

15 pages, no figures, LaTeX. To appear in Mathematische Zeitschrift

References in corpus (1)

• Some Rational Vertex Algebras