One way to study the Kronecker coefficients is to focus on the Kronecker cone, which is generated by the triples of partitions corresponding to non-zero Kronecker coefficients. In this article we are interested in producing particular faces of this cone, formed of stable triples (a notion defined by J. Stembridge in 2014), using some geometric notions—principally those of dominant and well-covering pairs—and results of N. Ressayre. This extends a result obtained independently by L. Manivel and E. Vallejo in 2014 or 2015, expressed in terms of additive matrices. To illustrate the fact that it allows to produce quite a few new faces of the Kronecker cone, we give at the end of the article details about what our results yield for “small dimensions”.

研究 Kronecker 系数的一种方法是关注 Kronecker 锥，它由对应于非零 Kronecker 系数的分区的三元组生成。在本文中，我们感兴趣的是使用一些几何概念（主要是占主导地位和覆盖良好的对的几何概念）以及 N 的结果，生成由稳定三元组（由 J. Stembridge 在 2014 年定义的概念）形成的锥体的特定面。复述。这扩展了 L. Manivel 和 E. Vallejo 在 2014 年或 2015 年独立获得的结果，以加法矩阵表示。为了说明它允许生成克罗内克锥的许多新面这一事实，我们在文章末尾详细说明了我们的结果对“小尺寸”产生的影响。