Title: A Higher Dimensional Bailey Lemma and
the Rogers-Ramanujan Identities
Abstract: Bailey Lemma is a powerful iterative method of proving $q$-series identities. An important application of this Lemma is the proof of the famous Rogers--Ramanujan identities. Higher dimensional generalizations of these identities have been actively pursued, yet the results obtained so far have not been satisfactory. A higher dimensional Bailey Lemma may be the first step to generalizing the Rogers--Ramanujan identities. We'll talk about such a generalization and an interpretation of the Bailey Lemma, and some recent progress and preliminary results towards proving a multiple generalization of the Rogers--Ramanujan identities.