On results of certain modules over untwisted affine Liesuperalgebras

TL;DR

This paper consolidates known results on modules over untwisted affine Lie superalgebras, building on recent studies of finite weight modules over twisted cases to aid future classification efforts.

Contribution

It compiles and clarifies existing results on modules over untwisted affine Lie superalgebras, facilitating further research in the area.

Findings

Known results on representations of untwisted affine Lie superalgebras are summarized.

Proofs for these results are minor modifications of twisted cases.

The compilation supports ongoing classification of modules.

Abstract

Since 2020, finite weight modules have been studied over twisted affine Lie superalgebras. To complete the characterization of modules over affine Lie superalgebras, we need some information regarding modules over untwisted affine Lie superalgebras. There are several known results on representations of twisted affine Lie superalgebras that hold for untwisted cases, and their proofs are just a minor modification of the known ones. In this note, we gather these results for our further use.