A family of irreducible representations of the Witt Lie algebra with infinite-dimensional weight spaces (Q2752524)

The authors construct a \(4\)-parameter family of representations of the Witt Lie algebra on which the infinitesimal rotation operator acts semisimply with countably infinite-dimensional weight spaces. These representations are generically irreducible and inequivalent. They can be viewed as deformations of generically indecomposable Feigin-Fuchs representations on spaces of polynomial differential operators between two spaces of tensor densities on \(S^1\), which are constructed by composing each such differential operator with the action of a rotation by a fixed angle.