# Finite weight modules over twisted affine Lie superalgebras

## TL;DR

This paper advances the understanding of finite weight modules over twisted affine Lie superalgebras by initiating their classification and linking some subclasses to known classifications of cuspidal modules.

## Contribution

It provides the first classification framework for irreducible finite weight modules over twisted affine Lie superalgebras, including cases where the central element acts non-trivially.

## Key findings

- Reduced classification of certain modules to known cuspidal superalgebra modules
- Established initial classification steps for these modules
- Connected module classification to existing superalgebra results

## Abstract

This work provides the first step toward the classification of irreducible finite weight modules over twisted affine Lie superalgebras. We study all such modules whether the canonical central element acts as a nonzero multiple of the identity map or not. Moreover, we reduce the classification of some subclasses of irreducible finite weight modules to the classification of cuspidal modules of finite dimensional cuspidal superalgebras which is known by a work of Dimitrov, Mathieu and Penkov.