New simple slˆ2-modules from Weyl algebra modules

We construct a class of modules over the affine Lie algebra slˆ2 from the modules over the degree-2 Weyl algebra K2 and modules over the 2-dimensional solvable Lie algebra b. We determine the irreducibility and isomorphisms of these modules with examples given by Bavula's construction of modules for generalized Weyl algebras in [5]. Finally, we show these irreducible slˆ2-modules are generally new.