Irreducible Representations of Wittenʹs Deformations ofU(sl2)

Using E. Wittenʹs approach based on duality in conformal field theory, one can obtain a 7-parameter family of deformations ofU(sl2) (called the “Wittenʹs Deformations”). Le Bruyn singled out a subfamily (called “conformalsl2algebras”) and studied their finite dimensional representations. Here we consider all of Wittenʹs deformations. We compute the left spectrum of these algebras and thereby classify irreducible representations for generic values of parameters and finite dimensional representations in certain “roots of unity” cases.