Séminaire Lotharingien de Combinatoire, B75d (2016), 14 pp.
Laurent Manivel
On the Asymptotics of Kronecker Coefficients, 2
Abstract.
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.
Received: January 1, 2016.
Accepted: February 9, 2016.
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