  In symmetric groups, a two-sided cell is the set of all permutations which
are mapped by the Robinson-Schensted correspondence on a pair of tableaux of
the same shape. In this article, we show that the set of permutations in a
two-sided cell which have a minimal number of inversions is the set of
permutations which have a maximal number of inversions in conjugated Young
subgroups. We also give an interpretation of these sets with particular
tableaux, called reading tableaux. As corollary, we give the set of elements in
a two-sided cell which have a maximal number of inversions.
