Production of faces of the Kronecker cone containing stable triples

Autor: Maxime Pelletier
Rok vydání: 2021
Předmět:
Zdroj: Geometriae Dedicata. 214:739-765
ISSN: 1572-9168
0046-5755
DOI: 10.1007/s10711-021-00634-x
Popis: 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”.
Databáze: OpenAIRE