A family of non-weight modules over the super-Virasoro algebras
Abstract
In this paper, we construct a family of non-weight modules over the super-Virasoro algebras. Those modules when regarded as modules of the Ramond algebra and further restricted as modules over the Cartan subalgebra $\mathfrak{h}$ are free of rank $1$, while when regarded as modules of the Neveu-Schwarz algebra and further restricted as modules over the Cartan subalgebra $\mathfrak{H}$ are free of rank $2$. We obtain a sufficient and necessary condition for such modules to be simple. Moreover, we determine the isomorphism classes of these modules. Finally, we show that these modules constitute a complete classification of free $U(\mathfrak{h})$-modules of rank $1$ over the super-Virasoro algebra of Ramond type, and also constitute a complete classification of free $U(\mathfrak{H})$-modules of rank $2$ over the super-Virasoro algebra of Neveu-Schwarz type.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.07129
- arXiv:
- arXiv:1906.07129
- Bibcode:
- 2019arXiv190607129Y
- Keywords:
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- Mathematics - Representation Theory
- E-Print:
- 17 pages