# Graded dimensions of principal subspaces and modular Andrews–Gordon-type series

#### 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 A (1) N−1, and of principal subspaces of certain higher level standard modules for A (1) 2n . Second, we establish the modular properties of families of q-series that appear in identities due to Warnaar and Zudilin, which generalize Macdonald’s A (2) 2n 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.

### Cite this paper

@inproceedings{Bringmann2014GradedDO, title={Graded dimensions of principal subspaces and modular Andrews–Gordon-type series}, author={Kathrin Bringmann and Corina Calinescu}, year={2014} }