We use Kashiwara-Nakashima's combinatorics of crystal graphs associated to the roots sytems $B_{ n}$ and $D_{ n}$ to extend the results of \QCITE{ cite}{ }{ lec3} and \QCITE{ cite}{ }{ Mor} by showing that Morris type recurrence formulas also exist for the orthogonal root systems. We derive from these formulas a statistic on Kashiwara-Nakashima's tableaux of types $B_{ n},C_{ n}$ and $D_{ n}$ generalizing Lascoux-Sch\UNICODE{ 0xfc}tzenberger's charge and from which it is possible to compute the Kostka-Foulkes polynomials $K_{ \lambda ,\mu}(q)$ with restrictive conditions on $(\lambda ,\mu)$ . This statistic is different from that obtained in \QCITE{ cite}{ }{ lec3} from the cyclage graph structure on tableaux of type $C_{ n}$. We show that such a structure also exists for the tableaux of types $B_{ n}$ and $D_{ n}$ but can not be simply related to the Kostka-Foulkes polynomials. Finally we give explicit formulas for $K_{ \lambda ,\mu}(q)$ when $| \lambda | \leq 3,$ or $n=2$ and $\mu =0$.
Categories: math.CO math.RT