  The Kronecker coefficients and the Littlewood-Richardson coefficients are
nonnegative integers depending on three partitions. By definition, these
coefficients are the multiplicities of the tensor product decomposition of two
irreducible representations of symmetric groups (resp. linear groups). By a
classical Littlewood-Murnaghan's result the Kronecker coefficients extend the
Littlewood-Richardson ones.The nonvanishing of a Littlewood-Richardson
coefficient implies linear inequalities on the triple of partitions, called
Horn inequalities. In thispaper, we extend the essential Horn inequalities to
the triples of partitions corresponding to a nonzero Kronecker coefficient.
