Multiparameter Bailey Pairs and Rogers-Ramanujan-Slater Identities

It is well known that the analytic and combinatorial generalizations of the Rogers-Ramanujan identities due to Andrews, Gordon, and Bressoud explain the standard modules associated with the various levels of A(1) 1 . From the analytic/combinatorial perspective, the Andrews-Gordon-Bressoud identities may be generated by building a “Bailey chain” from the so-called “unit Bailey pair” and considering associated q-difference equations. I will show how just a few multiparameter Bailey pairs and their associated q-difference equations are sufficient to generate more that half of the 130 Rogers-Ramanujan type identities included in Lucy Slater’s famous list, reveal many new Rogers-Ramanujan type identities, and provide natural combinatorial interpretations for the analytic identities.