Quasi-integrable modules, a class of non-highest weight modules over twisted affine Lie superalgebras

TL;DR

This paper characterizes quasi-integrable modules over twisted affine Lie superalgebras, showing they are not always highest weight and can be constructed via parabolic induction from cuspidal modules, simplifying their classification.

Contribution

It provides a new characterization and classification approach for quasi-integrable modules, linking them to cuspidal modules over finite-dimensional Lie superalgebras.

Findings

Quasi-integrable modules are not necessarily highest weight.

They are parabolically induced from cuspidal modules.

Classification reduces to known cuspidal module classification.

Abstract

In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that quasi-integrable modules are not necessarily highest weight modules. We prove that each 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 quasi-integrable modules is reduced to the known classification of cuspidal modules over such Lie superalgebras.