HALL-LITTLEWOOD FUNCTIONS AND KOSTKA-FOULKES POLYNOMIALS AT ROOTS OF UNITY

We investigate the specialization at roots of unity of modified Hall-Littlewood functions. We show that these functions admit a factorization property. The simple factors are complete symmetric functions in the k-th powers of the variables. It follows that the decomposition coefficients of the preceding plethysms are specializations of Kostka-Foulkes polynomials at a primitive k-th root of unity.