On the asymptotics of Kronecker coefficients - Archive ouverte HAL Access content directly
Journal Articles Journal of Algebraic Combinatorics Year : 2015

On the asymptotics of Kronecker coefficients

Laurent Manivel


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). We describe a geometric method, based on Schur-Weyl duality, that allows to produce huge series of instances of this phenomenon. Moreover the method gives access to lots of extra information. Most notably, we can often compute the stable Kronecker coefficients, sometimes as number of points in very explicit polytopes. We can also describe explicitely the moment polytope in the neighbourhood of our stable triples. Finally, we explain an observation of Stembridge on the behaviour of certain rectangular Kronecker coefficients, by relating it to the affine Dynkin diagram of type $E_6$.
Fichier principal
Vignette du fichier
asympKron.pdf (211.99 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01082218 , version 1 (12-11-2014)



Laurent Manivel. On the asymptotics of Kronecker coefficients. Journal of Algebraic Combinatorics, 2015, 42 (4), pp.999-1025. ⟨hal-01082218⟩
65 View
447 Download



Gmail Facebook X LinkedIn More