Annihilating fields of standard modules for affine Lie algebras (Q5947790)

The paper under review provides a vertex-algebraic framework for studying representation theory of affine Kac-Moody Lie algebras of twisted type. The author presents many important results which generalize those obtained in the untwisted case by \textit{A. Meurman} and \textit{M. Primc} [Mem. Am. Math. Soc. 652 (1999; Zbl 0918.17018)]. Let \(\widetilde{\mathfrak{g}}[\sigma]\) be an affine Kac-Moody Lie algebra. The author investigates restricted \(\widetilde{\mathfrak{g}}[\sigma]\)-modules of level \(k\) as twisted modules for the vertex operator algebra \(N(k\Lambda_0)\). Then he applies the results and constructions on twisted modules obtained by \textit{H. Li} [Contemp. Math. 193, 203--236 (1996; Zbl 0844.17022)]. The author also introduces an irreducible integrable loop \(\widetilde{\mathfrak{g}}[\sigma]\)-module \(\overline{R}_{\sigma}\) which is associated to a singular vector in the vertex operator algebra \(N(k \Lambda_0)\). He proves proves that a highest weight \(\widetilde{\mathfrak{g}}[\sigma]\)-module \(M\) of positive integer level \(k\) is a standard module if and only if \(\overline{R}_{\sigma} M =0\). This result is very useful in the study of annihilating fields of highest weight representations and it has interesting combinatorial consequences.