An example of A2$A_2$ Rogers–Ramanujan bipartition identities of level 3

Abstract We give manifestly positive Andrews–Gordon type series for the level 3 standard modules of the affine Lie algebra of type . We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel–Welsh recursion for the cylindric partitions, a ‐version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author.