Fonctions de Hall-Littlewood et polynômes de Kostka-Foulkes aux racines de l’unité. (Hall-Littlewood functions and Kostka-Foulkes polynomials at roots of unity). (French) Zbl 0769.05095
Summary: 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.
MSC:
05E05 | Symmetric functions and generalizations |