  Kanade and Russell conjectured several Rogers-Ramanujan-type partition
identities, some of which are related to level $2$ characters of the affine Lie
algebra $A_9^{(2)}$. Many of these conjectures have been proved by Bringmann,
Jennings-Shaffer and Mahlburg. We give new proofs of five conjectures first
proved by those authors, as well as four others that have been open until now.
Our proofs for the new cases use quadratic transformations for Askey-Wilson and
Rogers polynomials. We also obtain some related results, including a new proof
of a partition identity conjectured by Capparelli and first proved by Andrews.
