Annihilating Fields of Standard Modules for Affine Lie Algebras

Details Annihilating Fields of Standard Modules for Affine Lie Algebras Annihilating Fields of Standard Modules for Affine Lie Algebras

2001-05-03

arxiv.org/abs/math/0105021v1

Mathematische Zeitschrift 237 (2001), 301-319

Mathematics

Quantum Algebra

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

Scientific paper

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.

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