Abstract. The two Rogers-Ramanujan q-serieswhere σ = 0, 1, play many roles in mathematics and physics. By the Rogers-Ramanujan identities, they are essentially modular functions. Their quotient, the Rogers-Ramanujan continued fraction, has the special property that its singular values are algebraic integral units. We find a framework which extends the Rogers-Ramanujan identities to doublyinfinite families of q-series identities. If a ∈ {1, 2} and m, n ≥ 1, then we have λ λ1≤mwhere the P λ (x 1 , x 2 , . . . ; q) are Hall-Littlewood polynomials. These q-series are specialized characters of affine Kac-Moody algebras. Generalizing the Rogers-Ramanujan continued fraction, we prove in the case of A2n that the relevant q-series quotients are integral units.