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

TL;DR

This paper derives q-difference equations for graded dimensions of principal subspaces in higher-level standard modules of bsl(3), providing new formulas for these dimensions using vertex operator algebra techniques.

Contribution

It introduces a novel approach using vertex operator algebras to compute graded dimensions of principal subspaces in bsl(3) modules, resulting in explicit formulas.

Findings

Derived q-difference equations for graded dimensions.

Established new formulas for principal subspace dimensions.

Connected vertex operator algebra theory with combinatorial identities.

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 i\Lambda_1+(k-i)\Lambda_2, where 1 \leq i \leq k and \Lambda_1 and \Lambda_2 are fundamental weights of \hat{\goth{sl}(3)}.