# Snowflake modules and Enright functor for Kac-Moody superalgebras

## TL;DR

This paper introduces snowflake modules for Kac-Moody superalgebras, characterized by their character invariance, and uses them to prove Arakawa's Theorem for osp(1|2n).

## Contribution

It defines a new class of modules called snowflake modules and applies them to advance the understanding of representation theory for superalgebras.

## Key findings

- Snowflake modules exhibit character invariance under a Weyl subgroup.
- Examples include admissible modules in affine vertex algebra representations.
- Application to prove Arakawa's Theorem for osp(1|2n).

## Abstract

We introduce a class of modules over Kac-Moody superalgebras; we call these modules snowflake. 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 classification of bounded weight modules. Using these modules we prove Arakawa's Theorem for the Lie superalgebra osp(1|2n).