Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system $C_n$

Abstract

We establish a Morris type recurrence formula for the root system $C_n$.\ Next we introduce cyclage graphs for the corresponding Kashiwara-Nakashima's tableaux and use them to define a charge statistic. Finally we conjecture that this charge may be used to compute the Kostka-Foulkes polynomials for type $C_n.$