On the asymptotics of Kronecker coefficients, 2

Abstract

Kronecker coefficients encode the tensor products of complex irreducible\nrepresentations of symmetric groups. Their stability properties have been\nconsidered recently by several authors (Vallejo, Pak and Panova, Stembridge).\nIn previous works we described a geometric method, based on Schur-Weyl duality,\nthat allows to produce huge series of instances of this phenomenon. In this\nnote we show how to go beyond these so-called additive triples. We show that\nthe set of stable triples defines a union of faces of the moment polytope.\nMoreover these faces may have different dimensions, and many of them have\ncodimension one.\n