Background
Type: Article

Quasi-Integrable Modules over Twisted Affine Lie Superalgebras: Quasi-Integrable Modules: Yousofzadeh M.

Journal: Transformation Groups (1531586X)Year: December 2024Volume: 29Issue: Pages: 1699 - 1720
DOI:10.1007/s00031-023-09805-4Language: English

Abstract

In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that these form a class of not necessarily highest weight modules. We prove that each nonzero level quasi-integrable module is parabolically induced from a cuspidal module, over a finite dimensional Lie superalgebra having a Cartan subalgebra whose corresponding root system just contain real roots; in particular, the classification of nonzero level quasi-integrable modules is reduced to the known classification of cuspidal modules over such Lie superalgebras. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.