Proofs and reductions of various conjectured partition identities of Kanade and Russell

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 A9(2). We also give reductions of four other conjectures in terms of single-sum basic hypergeometric series.