2018/05/25 by Maxime Pelletier, Pelletier, Maxime
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1805.10218
openalex publication_date 2018/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 many 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 matrix. 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".