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Mathematics > Algebraic Geometry

arXiv:1805.10218 (math)
[Submitted on 25 May 2018]

Title:Production of faces of the Kronecker cone containing only stable triples

Authors:Maxime Pelletier (ICJ)
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Abstract: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".
Subjects: Algebraic Geometry (math.AG); Representation Theory (math.RT)
Cite as: arXiv:1805.10218 [math.AG]
  (or arXiv:1805.10218v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.10218

Submission history

From: Maxime Pelletier [view email] [via CCSD proxy]
[v1] Fri, 25 May 2018 15:55:49 UTC (21 KB)
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