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Register a new userA Geometric Approach to the stabilisation of certain sequences of Kronecker coefficients
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Authors
Maxime Pelletier
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We give another proof, 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 Murnaghans 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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The computation of Kronecker coefficients is a challenging problem with a variety of applications. In this paper we present an approach based on methods from symplectic geometry and residue calculus. We outline a general algorithm for the problem and then illustrate its effectiveness in several interesting examples. Significantly, our algorithm does not only compute individual Kronecker coefficients, but also symbolic formulas that are valid on an entire polyhedral chamber. As a byproduct, we are able to compute several Hilbert series.
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