On characters of L𝔰𝔩n(−Λ0)-modules

We use recent results of Rolen, Zwegers, and the first author to study the characters of irreducible (highest weight) modules for the vertex operator algebra [Formula: see text]. We establish asymptotic behaviors of characters for the (ordinary) irreducible [Formula: see text]-modules. As a consequence, we prove that their quantum dimensions are one, as predicted by the representation theory. We also establish a full asymptotic expansion of irreducible characters for [Formula: see text]. Finally, we determine a decomposition formula for the full characters in terms of unary theta and false theta functions which allows us to study their modular properties.