Zero-level integrable modules over twisted affine Lie superalgebras

TL;DR

This paper characterizes zero-level integrable finite weight modules over twisted affine Lie superalgebras, showing they are parabolically induced from modules over certain Lie algebras, and provides a complete classification of these modules.

Contribution

It offers a new classification of zero-level integrable modules over twisted affine Lie superalgebras, linking them to modules over abelian and quadratic Lie superalgebras.

Findings

Modules are parabolically induced from modules over specific Lie algebras.

Complete classification of finite dimensional simple quadratic Lie superalgebra modules.

Characterization of bounded finite weight modules over quadratic Lie superalgebras.

Abstract

The main result of this paper is the characterization of zero-level integrable finite weight modules, over twisted affine Lie superalgebras. We prove that such a module is parabolically induced from a module which is obtained, in a prescribed way, from a module over a Lie algebra $\mathscr{L}$ which is either a $\bbbz$-graded abelian Lie algebra or a direct sum of a $\bbbz$-graded abelian Lie algebra and the so-called quadratic Lie superalgebra $\mathcal{Q}$. We give also a complete characterization of both finite dimensional simple $\mathcal{Q}$-modules as well as bounded finite weight $\bbbz$-graded simple $\mathcal{Q}$-modules.