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

2016/06/17 by Maxime Pelletier, Pelletier, Maxime
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1606.05475

openalex publication_date 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem
• Geometric quantization and multiplicities of group representations

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• On the asymptotics of Kronecker coefficients, 2
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• Conjectures on the reduced Kronecker coefficients
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