Quasi-Integrable Modules over Twisted Affine Lie Superalgebras

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...

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Bibliographic Details
Published in:Transformation groups 2024-12, Vol.29 (4), p.1699-1720
Main Author: Yousofzadeh, Malihe
Format: Article
Language:English
Subjects:
Classification
Modules
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Summary: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.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-023-09805-4