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Quasi-Integrable Modules over Twisted Affine Lie Superalgebras

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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.

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Data Availability

The datasets generated during or analysed during the current study are available from the corresponding author on reasonable request.

Notes

  1. We use \(\#\) to indicate the cardinal number.

  2. It is the subalgebra of all diagonal matrices.

  3. In Proposition 3.7 of [23], we are working with \(\mathfrak {L}\) or \(\mathfrak {L}_0\) instead of \(\mathscr {G}\) introduced here, but our assumptions on T make the same situation as in Proposition 3.7 of [23].

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Acknowledgements

This research was in part supported by a grant from IPM (No. 1400170215) and is partially carried out in IPM-Isfahan Branch. This work is based upon research funded by Iran Nathional Science Foundation INSF (No. 4001480).

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441, Isfahan, Iran

    Malihe Yousofzadeh

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran

    Malihe Yousofzadeh

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  1. Malihe Yousofzadeh
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Yousofzadeh, M. Quasi-Integrable Modules over Twisted Affine Lie Superalgebras. Transformation Groups (2023). https://doi.org/10.1007/s00031-023-09805-4

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