Andrews-Gordon style identities

In a recent paper, Griffin, Ono and Warnaar present a framework for Rogers-Ramanujan type identities using extended Hall-Littlewood polynomials Pλ(x1,x2,…;q) to arrive at expressions of the form $$\sum\limits_{\lambda : \lambda_{1} \leq m} q^{a|\lambda|}P_{2\lambda}(1,q,q^{2},\ldots ; q^{n}) = \text{{\textquotedblleft}Infinite product modular function{\textquotedblright}} $$