Abstract
Our results in this paper are threefold: First, we establish the modular properties of the graded dimensions of principal subspaces of level one standard modules for [Formula: see text], and of principal subspaces of certain higher level standard modules for [Formula: see text]. Second, we establish the modular properties of families of q-series that appear in identities due to Warnaar and Zudilin, which generalize Macdonald's [Formula: see text] identities and the Rogers–Ramanujan identities. Third, we formulate a number of conjectures regarding the modularity of series of this type related to AN-1 root systems.
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