An A$_2$ Bailey lemma and Rogers--Ramanujan-type identities
  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. 
George E. Andrews, Anne Schilling, and S. Ole Warnaar