Green Polynomials and Hall-Littlewood Functions at Roots of Unity

Abstract

We give some applications of our recent work [10] about Hall-Littlewood functions at roots of unity. In particular, we prove the two conjectures of N. Sultana [17] on specializations of Green polynomials, and we generalize classical results concerning characters of the symmetric group induced by maximal cyclic subgroups. We also give some new congruences for Kostka-Foulkes polynomials modulo cyclotomic polynomials.