The partition algebra and the Kronecker coefficients

Abstract

We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition algebra. Our analysis leads to a uniform description of the Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition.

This version contains a uniform description of the Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition

References in corpus (4)

• Quantum marginal problem and representations of the symmetric group
• The stability of the Kronecker products of Schur functions
• Geometric Complexity Theory VI: the flip via saturated and positive integer programming in representation theory and algebraic geometry
• Momentum spectrometry of spherical harmonics and a probe of geometric embedding effect

Cited by in corpus (5)

• On the complexity of computing Kronecker coefficients
• Kronecker products, characters, partitions, and the tensor square conjectures
• Deligne categories and reduced Kronecker coefficients
• A Survey of Representation Stability Theory
• Double Macdonald polynomials as the stable limit of Macdonald superpolynomials