The partition algebra and the Kronecker coefficients

TL;DR

This paper introduces a novel approach using the partition algebra and Schur-Weyl duality to analyze Kronecker coefficients, providing uniform descriptions for specific cases and exploring their limiting behavior.

Contribution

It presents a new framework connecting partition algebra with Kronecker coefficients, offering insights into their bounds and asymptotic properties.

Findings

Uniform description of Kronecker coefficients for hook and two-part partitions

Analysis of limiting behavior and bounds of Kronecker coefficients

Establishment of a connection between partition algebra and symmetric group representations

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.