(Quasi-)admissible modules over symmetrizable Kac-Moody superalgebras

TL;DR

This paper extends the theory of admissible modules to all symmetrizable Kac-Moody superalgebras, broadening its applicability in representation theory and related areas.

Contribution

It generalizes the existing theory of admissible modules from anisotropic cases to all symmetrizable Kac-Moody superalgebras.

Findings

Extended admissible module theory to arbitrary symmetrizable Kac-Moody superalgebras.

Provided new frameworks for representation theory applications.

Connected the theory with recent developments by Gorelik and Serganova.

Abstract

The theory of admissible modules over symmetrizable anisotropic Kac-Moody superalgebras, introduced by Kac and Wakimoto in late 80's, is a well-developed subject with many applications, including representation theory of vertex algebras. Recently this theory was developed in a more general setup by Gorelik and Serganova. In the present paper we develop in this more general setup the theory of admissible modules over arbitrary symmetrizable Kac-Moody superalgebras.