Abstract
We prove seven of the Rogers–Ramanujan-type identities modulo 12 that were conjectured by Kanade and Russell. Included among these seven are the two original modulo 12 identities, in which the products have asymmetric congruence conditions, as well as the
three symmetric identities related to the principally specialized characters of certain level 2 modules of
Funding statement: The research of the first author is supported by the Alfried Krupp Prize for Young University Teachers of the Krupp foundation and the research leading to these results receives funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant agreement no. 335220 – AQSER.
Acknowledgements
We thank Shashank Kanade, Jim Lepowsky, Jeremy Lovejoy, and the anonymous referee for helpful comments on a preliminary version of this paper.
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