Proof of Stembridge's conjecture on stability of Kronecker coefficients

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.

8 pages, v2: Added references, Remark 4.5, and Section 4.3 on stability result for plethysms

References in corpus (4)

• Introduction to twisted commutative algebras
• Hilbert series for twisted commutative algebras
• Bounds on the Kronecker coefficients
• Multiplicity of compact group representations and applications to Kronecker coefficients

Cited by in corpus (6)

• Stability phenomena in the homology of tree braid groups
• Multiplicity of compact group representations and applications to Kronecker coefficients
• The Bosonic-Fermionic Diagonal Coinvariant Modules Conjecture
• All Kronecker coefficients are reduced Kronecker coefficients
• Production of faces of the Kronecker cone containing only stable triples
• A Survey of Representation Stability Theory