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arxiv: 1210.5579 · v6 · pith:FAXUGE2Knew · submitted 2012-10-20 · 🧮 math.RT · math.CO

The partition algebra and the Kronecker coefficients

Christopher Bowman , Maud De Visscher , Rosa Orellana This is my paper
classification 🧮 math.RT math.CO
keywords partitionalgebracoefficientskroneckeranalysisapproachassociatedbehavior
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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.

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  1. Semisimplicity criterion for 2-tonal partition algebras

    math.RT 2026-04 unverdicted novelty 7.0

    Even partition algebras P_n^2(δ) over ℂ are semisimple for all n if and only if δ is not a non-negative integer.