Séminaire Lotharingien de Combinatoire, 89B.38 (2023), 12 pp.
Shashank Kanade
On the A2 Andrews-Schilling-Warnaar Identities
Abstract.
In a groundbreaking work, Andrews-Schilling-Warnaar invented an A2 generalization of the A1 Bailey machinery and discovered many identities related to the principal characters of standard modules for sl^3, or equivalently, for the vertex operator algebra W3(3,p'). Jointly with Russell, we have given conjectures for completing this set of identities and proved these conjectures for small values of p'. In another direction, character of Wr(p,p') has been related to an appropriate limit of certain sl^r coloured Jones polynomials of torus knots T(p,p') under some restrictions on r,p,p'. This note summarizes these developments.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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