A stability property for coefficients in Kronecker products of complex S_n characters

TL;DR

This paper reveals a stability property of Kronecker coefficients related to symmetric group characters, providing a new formula and clarifying an implicit aspect of prior theoretical work.

Contribution

It explicitly states a stability property for Kronecker coefficients, overlooked in previous research, and derives a new formula for certain coefficients.

Findings

Identifies an explicit stability property for Kronecker coefficients.

Provides a new formula for specific Kronecker coefficients.

Clarifies an implicit stability property in Dvir's theorem.

Abstract

In this note we make explicit a stability property for Kronecker coefficients that is implicit in a theorem of Y. Dvir. Even in the simplest nontrivial case this property was overlooked despite of the work of several authors. As an application we give a new formula for some Kronecker coefficients.