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arXiv · 1809.08128

The partition algebra and the plethysm coefficients I: stability and Foulkes' conjecture

Chris Bowman·Rowena Paget
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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.

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Chris Bowman, Rowena Paget. 2018-09-21. The partition algebra and the plethysm coefficients I: stability and Foulkes' conjecture. https://arxiv.org/abs/1809.08128

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