Shashank Kanade (Denver)
Abstract
Principal characters of standard (i.e., highest weight, integrable) modules for affine Lie algebras have been a rich source of q-series and partition identities. The algebra A_1^{(1)} (or, sl_2^) was "understood" in this sense a few decades ago. On q-series side, this leads to identities of Gordon-Andrews and Andrews-Bressoud. In this talk, I'll present q-series identities related to the next "simplest" affine Lie algebra, namely, A_2^{(2)}. Here, we get six families of q-series identities confirming a conjecture of McLaughlin and Sills. The main machinery used is that of Bailey pairs and Bailey lattices. This is a joint work with Matthew C. Russell.