Modular units from quotients of Rogers-Ramanujan type 𝑞-series

In recent work, Folsom presents a family of modular units as higher-level analogues of the Rogers-Ramanujan q q -continued fraction. These units are constructed from analytic solutions to the higher-order q q -recurrence equations of Selberg. Here, we consider another family of modular units, which are quotients of Hall-Littlewood q q -series that appear in the generalized Rogers-Ramanujan type identities in the work of Griffin, Ono, and Warnaar. In analogy with the results of Folsom, we provide a formula for the rank of the subgroup these units generate and show that their specializations at the cusp 0 0 generate a subgroup of the cyclotomic unit group of the same rank. In addition, we prove that their singular values generate the same class fields as those of Folsom’s units.