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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