New Identities for Hall-Littlewood Polynomials and Applications

Abstract

Starting from Macdonald's summation formula of Hall-Littlewood polynomials over bounded partitions and its even partition analogue, Stembridge (Trans. Amer. Math. Soc., 319(2), (1990) 469–498) derived sixteen multiple q-identities of Rogers–Ramanujan type. Inspired by our recent results on Schur functions (Adv. Appl. Math., 27, (2001) 493–509) and based on computer experiments we obtain two further such summation formulae of Hall-Littlewood polynomials over bounded partitions and derive six new multiple q-identities of Rogers–Ramanujan type.