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The partition algebra and the plethysm coefficients I: stability and Foulkes' conjecture (1809.08128v2)
Published 21 Sep 2018 in math.RT and math.CO
Abstract: We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This allows us to explain the stability properties of plethysm and Kronecker coefficients in a simple and uniform fashion for the first time. We prove the strengthened Foulkes' conjecture for stable plethysm coefficients in an elementary fashion.