Geodesic
On the Asymptotics of Kronecker Coefficients, 2
Séminaire lotharingien de combinatoire, Tome 75 (2016-2019)

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Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). In [J. Alg. Combin. 42 (2015), 999-1025], we described a geometric method, based on Schur-Weyl duality, that allows one to produce huge series of instances of this phenomenon. In this note, we show how to go beyond these so-called additive triples. We show that the set of stable triples defines a union of faces of the cone generated by the supports of the nonzero Kronecker coefficients. Moreover, these faces may have different dimensions, and many of them have codimension one. 

@article{SLC_2016-2019_75_a3,
     author = {Laurent Manivel},
     title = {On the {Asymptotics} of {Kronecker} {Coefficients,} 2},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {75},
     year = {2016-2019},
     url = {http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a3/}
}
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Laurent Manivel. On the Asymptotics of Kronecker Coefficients, 2. Séminaire lotharingien de combinatoire, Tome 75 (2016-2019). http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a3/