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 $A_9^{\left(2\right)}$. We also give reductions of four other conjectures in terms of single-sum basic hypergeometric series.

中文翻译：

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Kanade和Russell的各种猜想分区身份的证明和约简

我们证明了Kanade和Russell猜想的7个模数为12的Rogers-Ramanujan型身份。这七个中包括两个原始的模12身份，其中的乘积具有不对称的一致条件，以及三个对称的身份，它们与某些2级模块的主要专业特征有关${\mathrm{一种}}_9^{（2）}$。根据单和基本超几何序列，我们还给出了其他四个猜想的简化。