An A$_2$ Bailey lemma and Rogers--Ramanujan-type identities

TL;DR

This paper introduces a new A_2 Bailey lemma using recently developed q-functions and applies it to derive Rogers-Ramanujan-type identities for W_3 algebra characters, expanding the theoretical framework of q-series identities.

Contribution

It presents a novel A_2 Bailey lemma based on new q-functions, distinct from previous versions, and applies it to obtain new Rogers-Ramanujan-type identities.

Findings

Derived new Rogers-Ramanujan-type identities for W_3 algebra characters

Introduced an A_2 Bailey lemma using recent q-functions

Distinct from existing A_2 Bailey lemmas of Milne and Lilly

Abstract

Using new $q$-functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A_2 version of the classical Bailey lemma. We apply our result, which is distinct from the A_2 Bailey lemma of Milne and Lilly, to derive Rogers-Ramanujan-type identities for characters of the W_3 algebra.