A remark on boundary level admissible representations
Representation Theory
2016-12-23 v1
Abstract
Recently a remarkable map between 4-dimensional superconformal field theories and vertex algebras has been constructed \cite{BLLPRV15}. This has lead to new insights in the theory of characters of vertex algebras. In particular it was observed that in some cases these characters decompose in nice products \cite{XYY16}, \cite{Y16}. The purpose of this note is to explain the latter phenomena. Namely, we point out that it is immediate by our character formula \cite{KW88}, \cite{KW89} that in the case of a \textit{boundary level} the characters of admissible representations of affine Kac-Moody algebras and the corresponding -algebras decompose in products in terms of the Jacobi form .
Cite
@article{arxiv.1612.07423,
title = {A remark on boundary level admissible representations},
author = {Victor G. Kac and Minoru Wakimoto},
journal= {arXiv preprint arXiv:1612.07423},
year = {2016}
}