A generalization of partition identities of Göllnitz-Gordon, Rogers-Ramanujan and Nandi

Abstract

We propose Andrews-Gordon type series for certain level 2 standard modules of type $A^{(2)}_{\textrm{odd}}$, and prove the corresponding sum-product identities except for $A^{(2)}_{6n+3}$. These identities generalize the identities of Göllnitz-Gordon (mod 8), Rogers-Ramanujan (mod 5) and (partially) Nandi (mod 14).