Christopher Bowman, Maud De Visscher, Rosa Orellana
Published 2012-10-20, updated 2013-02-25Version 6
We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition algebra. Our analysis leads to a uniform description of the Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition.
Comments: This version contains a uniform description of the Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition
Partition algebras $\mathsf{P}_k(n)$ with $2k>n$ and the fundamental theorems of invariant theory for the symmetric group $\mathsf{S}_n$
Partition Algebras and the Invariant Theory of the Symmetric Group
Kronecker Coefficients and Harrison Centers of Green's Ring $\mathcal{R}(S_6)$
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