On the Kanade-Russell identities

Abstract: Kanade and Russell conjectured several Rogers-Ramanujan-type identities for triple series. Some of these conjectures are related to characters of affine Lie algebras, and they can all be interpreted combinatorially in terms of partitions. Many of these conjectures were settled by Bringmann, Jennings-Shaffer and Mahlburg. We describe a new approach to the Kanade-Russell identities, which leads to new proofs of five previously known identities, as well as four identities that were still open. For the new cases, we need quadratic transformations for q-orthogonal polynomials.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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