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Pré-Publication, Document De Travail Année : 2016

A Geometric Approach to the stabilisation of certain sequences of Kronecker coefficients

Résumé

We give another demonstration, using tools from Geometric Invariant Theory, of a result due to S. Sam and A. Snowden in 2014, concerning the stability of Kro-necker coefficients. This result states that some sequences of Kronecker coefficients eventually stabilise, and our method gives a nice geometric bound from which the stabilisation occurs. We perform the explicit computation of such a bound on two examples, one being the classical case of Murnaghan's stability. Moreover, we see that our techniques apply to other coefficients arising in Representation Theory: namely to some plethysm coefficients and in the case of the tensor product of representations of the hyperoctahedral group.
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Dates et versions

hal-01332900 , version 1 (17-06-2016)
hal-01332900 , version 2 (01-07-2016)
hal-01332900 , version 3 (13-04-2018)

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Maxime Pelletier. A Geometric Approach to the stabilisation of certain sequences of Kronecker coefficients. 2016. ⟨hal-01332900v2⟩
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