A classical $q$-hypergeometric approach to the standard $A_2^{(2)}$ standard modules

Abstract

This is a written expansion of the talk delivered by the author at the International Conference on Number Theory in Honor of Krishna Alladi for his 60th Birthday, held at the University of Florida, March 17--21, 2016. Here we derive Bailey pairs that give rise to Rogers--Ramanujan type identities which are the principally specialized character of the $A_2^{(2)}$ standard module $(\ell - 2i+2)\Lambda_0 + (i-1)\Lambda_1$ for any level $\ell$, and $i=1, 2$.}