Hall-Littlewood Functions, Plane Partitions, and the Rogers-Ramanujan Identities

We apply the theory of Hall-Littlewood functions to prove several multiple basic hypergeometric series identities, including some previously known generalizations of the Rogers-Ramanujan identities due to G. E. Andrews and D. M. Bressoud.The techniques involve the adaptation of a method due to I. G. Macdonald for calculating partial fraction expansions of certain types of symmetric formal power series.Macdonald originally used this method to prove a pair of generating function identities for plane partitions conjectured by MacMahon and Bender-Knuth.We show that this method can also be used to prove another pair of plane partition identities recently obtained by R. A. Proctor.