Abstract
AbstractKanade and Russell conjectured several Rogers–Ramanujan-type partition identities, some of which are related to level 2 characters of the affine Lie algebra $$A_9^{(2)}$$
A
9
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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 partition identity conjectured by Capparelli and first proved by Andrews.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference24 articles.
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5. Bringmann, K., Jennings-Shaffer, C., Mahlburg, K.: Proofs and reductions of various conjectured partition identities of Kanade and Russell. J. Reine Angew. Math. 766, 109–135 (2020)
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