Snowflake modules and Enright functor for Kac–Moody superalgebras

Abstract

We introduce a class of modules over Kac–Moody superalgebras; we call these modules snowflake modules. These modules are characterized by invariance property of their characters with respect to a certain subgroup of the Weyl group. Examples of snowflake modules appear as admissible modules in representation theory of affine vertex algebras and in the classification of bounded weight modules. Using these modules we prove Arakawa’s theorem for the Lie superalgebra $\mathfrak{o}\mathfrak{s}\mathfrak{p}{\left(1\right|2\ell )}^{\left(1\right)}$.