• 1 Instituto de Matematicas sede Morelia

In this paper we give a sufficient condition for a general stability of Kronecker coefficients, which we call additive stability. Its main ingredient is the property of a matrix of being additive. This notion seems to be an important one: it appears in Discrete Tomography as a sufficient condition to uniqueness; it also appears in Manivel’s study of asymptotic properties of plethysm through Borel-Weil theory. The proof sketched here combines several results of the author on integer matrices motivated by Discrete Tomography with a new idea of Stembridge, that permits to bound some sequences of Kronecker coefficients. The advantage of additivity with respect to the previous approach by Stembridge is that it is very easy to produce new examples of additive matrices and, therefore, to produce many new examples of stability of Kronecker coefficients. We also show that Murnaghan’s stability property and other instances of stability discovered previously by the author are special cases of additive stability. Besides, our approach permits us to disprove a recent conjecture of Stembridge and to give a new characterization of additivity.