Principal subspaces of higher-level standard image-modules

We use the theory of vertex operator algebras and intertwining operators to obtain systems of q-difference equations satisfied by the graded dimensions of the principal subspaces of certain level k standard modules for image. As a consequence we establish new formulas for the graded dimensions of the principal subspaces corresponding to the highest weights iΛ1+(k−i)Λ2, where 1≤i≤k and Λ1 and Λ2 are fundamental weights of image.