Interwining Operators for Vertex Representations of Toroidal Lie Algebras

The construction of the vertex representation of the toroidal Lie algebra ^[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 .