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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