A new class of modules for toroidal Lie superalgebras (Q1949999)

Toroidal Lie superalgebras are universal central extensions of Lie superalgebras of the form \(\mathfrak{g}\otimes A\), where \(\mathfrak{g}\) is a basic classical Lie superalgebra and \(A\) is a Laurent polynomial ring in several variables. In this paper the author constructs a new class of modules for toroidal Lie superalgebras by tensoring the standard Fock space for a suitable non-degenerate lattice and a degenerate sublattice with a restricted module \(V\) over the affine superalgebra corresponding to \(\mathfrak{g}\). It is shown that this construction is functorial in \(V\). It is also shown that several properties of \(V\) (e.g. being weight, integrable etc.) imply similar properties for the resulting module over the toroidal Lie superalgebra.