Interwining Operators for Vertex Representations of Toroidal Lie Algebras

The construction of the vertex representation of the toroidal Lie algebra τ[n] depends on the way of labelling the points in the dual n of the torus Tn. Thus there is a built-in symmetry of the vertex representation with respect to the symmetry of Zn. In conjunction with this, the energy operator L0 gives rise to intertwining operators which reflect the symmetry of the vertex representation with respect to S1 action on τ.