Proof of Stembridge's conjecture on stability of Kronecker coefficients
Combinatorics
2016-01-08 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.1501.00333,
title = {Proof of Stembridge's conjecture on stability of Kronecker coefficients},
author = {Steven V Sam and Andrew Snowden},
journal= {arXiv preprint arXiv:1501.00333},
year = {2016}
}
Comments
8 pages, v2: Added references, Remark 4.5, and Section 4.3 on stability result for plethysms