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.
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Pelletier, M. A geometric approach to the stabilisation of certain sequences of Kronecker coefficients. manuscripta math. 158, 235–271 (2019). https://doi.org/10.1007/s00229-018-1021-4
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DOI: https://doi.org/10.1007/s00229-018-1021-4