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.

17 pages

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Cited by in corpus (9)

• A family of simple non-weight modules over the twisted $N=2$ superconformal algebra
• The Heisenberg-Virasoro Lie conformal superalgebra
• On non-weight representations of the $N=2$ superconformal algebras
• Measures and generalizations of dual Littlewood identities
• A class of non-weight modules over the super-BMS${}_3$ algebra
• Irreducible Modules for Super-Virasoro Algebras from Algebraic D-Modules
• On a family of non-weight modules over Virasoro-type Lie (super)algebras
• Simple non-weight modules over Lie superalgebras of Block type
• Non-weight modules over generalized Heisenberg-Virasoro algebra of rank two