New simple \(\widehat{\mathfrak{sl}}_2\)-modules from Weyl algebra modules (Q6052904)

Affine Lie algebras are extensively studied and very useful among the infinite-dimensional Kac-Moody algebras. The authors construct a class of modules over the affine Lie algebra \(\widehat{\mathfrak{sl}}_2\) from the modules over the degree-\(2\) Weyl algebra \(\mathcal{K}_2\) and modules over the \(2\)-dimensional solvable Lie algebra \(\mathfrak{b}\). The authors determine the irreducibility and isomorphisms of these modules. They also show that these irreducible \(\widehat{\mathfrak{sl}}_2\)-modules are generally new.