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 T n . Thus there is a built-in symmetry of the vertex representation with respect to the symmetry of Z n . In conjunction with this, the energy operator L 0 gives rise to intertwining operators which reflect the symmetry of the vertex representation with respect to S 1 action on τ.