Factorization formulas for MacDonald polynomials

In [LLT1], Lascoux, Leclerc and Thibon give some factorisation formulas for Hall-Littlewood functions when the parameter q is specialized at roots of unity. They also give formulas in terms of cyclic characters of the symmetric group. In this article, we give a generalization of these specializations for different versions of the Macdonald polynomials and we obtain similar formulas in terms of plethysms and cyclic characters. In the last section, we give congruence formulas for (q, t)-Kostka polynomials using Schur functions in the alphabet of the powers of the parameter t. We will mainly follow the notations of [M].