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.
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Acknowledgments
We thank Greta Panova, Mateusz Michałek, John Stembridge, and Ernesto Vallejo for helpful comments and references.
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SS was supported by a Miller research fellowship. AS was supported by NSF Grant DMS-1303082.
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Sam, S.V., Snowden, A. Proof of Stembridge’s conjecture on stability of Kronecker coefficients. J Algebr Comb 43, 1–10 (2016). https://doi.org/10.1007/s10801-015-0622-1
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DOI: https://doi.org/10.1007/s10801-015-0622-1