Level three standard modules for A2(2) and combinatorial identities Original Research Article

We use the Z-algebra theory developed by J. Lepowsky and R. Wilson to study the structure of level three standard modules for the affine Lie algebra A2(2) in the principal picture. We get their linear bases in terms of Z-operators. As a consequence we give Z-algebra proofs of the conjectures of Capparelli (1993) on two combinatorial identities.