New Identities of Hall-Littlewood Polynomials and Rogers-Ramanujan Type

where a = 0 or 1, are among the most famous q-series identities in partitions and combinatorics. Since their discovery the Rogers-Ramanujan identities have been proved and generalized in various ways (see [2, 4, 5, 13] and the references cited there). In [13], by adapting a method of Macdonald for calculating partial fraction expansions of symmetric formal power series, Stembridge gave an unusual proof of Rogers-Ramanujan identities as well as fourteen other non trivial q-series identities of Rogers-Ramanujan type and their multiple analogs. Although it is possible to describe his proof within the setting of q-series, two summation formulas of Hall-Littlewood polynomials were a crucial source of inspiration for such kind of identities. One of our original motivations was to look for new multiple q-identities of Rogers-Ramanujan type through this approach, but we think that the new