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

Maxime Pelletier (1, 2, 3)

1 AGL - Algèbre, géométrie, logique
2 Université de Lyon
3 UCBL - Université Claude Bernard Lyon 1

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 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.

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Maxime Pelletier. A Geometric Approach to the stabilisation of certain sequences of Kronecker coefficients. Manuscripta mathematica, 2019, 158, pp.235-271. ⟨10.1007/s00229-018-1021-4⟩. ⟨hal-01332900v3⟩