Proof of Stembridge's conjecture on stability of Kronecker coefficients

TL;DR

This paper proves Stembridge's conjecture on the stability of Kronecker coefficients by linking them to Hilbert functions of modules, using only Schur-Weyl duality and Borel-Weil theorem, without relying on prior Kronecker coefficient work.

Contribution

It establishes a new proof of a conjecture on Kronecker coefficient stability, generalizing Murnaghan's theorem with a novel algebraic approach.

Findings

Proves Stembridge's conjecture on Kronecker coefficient stability

Links Kronecker coefficients to Hilbert functions of modules

Uses only Schur-Weyl duality and Borel-Weil theorem

Abstract

We prove a conjecture of Stembridge concerning stability of Kronecker coefficients that vastly generalizes Murnaghan's theorem. The main idea is to identify the sequences of Kronecker coefficients in question with Hilbert functions of modules over finitely generated algebras. The proof only uses Schur-Weyl duality and the Borel-Weil theorem and does not rely on any existing work on Kronecker coefficients.