A Family of Irreducible Representations of the Witt Lie Algebra with Infinite-Dimensional Weight Spaces

We define a 4-parameter family of generically irreducible and inequivalent representations of the Witt Lie algebra on which the infinitesimal rotation operator acts semisimply with infinite-dimensional eigenspaces. They are deformations of the (generically indecomposable) representations on spaces of polynomial differential operators between two spaces of tensor densities on S1, which are constructed by composing each such differential operator with the action of a rotation by a fixed angle.