Principal subspaces of higher-level standard sl(3)^-modules

Abstract

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 \hat{\goth{sl}(3)}. As a consequence we establish new formulas for the graded dimensions of the principal subspaces corresponding to the highest-weights iΛ_1+(k-i)Λ_2, where 1 \leq i \leq k and Λ_1 and Λ_2 are fundamental weights of \hat{\goth{sl}(3)}.