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A geometric approach to the stabilisation of certain sequences of Kronecker coefficients

  • Maxime Pelletier
Article

Abstract

We give another proof, using tools from Geometric Invariant Theory, of a result due to Sam and Snowden in (J Algebraic Comb 43(1):1–10, 2016), concerning the stability of Kronecker 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, as well as multiplicities for tensor products of representations of the hyperoctahedral group.

Mathematics Subject Classification

20G05 14L24 14L30 20C30 14M15 

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CNRS UMR 5208, Institut Camille JordanUniv Lyon, Université Claude Bernard Lyon 1Villeurbanne cedexFrance

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