[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 414/S-22, p. 27-35.]

The purpose of this paper is to prove an equidistribution
property for Young tableaux of a given form with respect to their
major indices modulo *n*. The same property holds for all
permutation statistics. Several other analogous results are also
derived.

We also derive the explict decomposition of the representation of
the symmetric group on the free Lie algebra associated with the
partition *n*. The latter result due to Kraskiewicz and Weyman is
quoted by Reutenauer.

We make use of the link of certain characters of the symmetric group with the major indices of Young tableaux, and also of a lemma of arithmetic nature.

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