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

Bowman, Christopher, Paget, Rowena (2023) The partition algebra and the plethysm coefficients I: stability and Foulkes' Conjecture. Journal of Algebra, . ISSN 0021-8693. (In press) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:102689)

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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 provides an explanation of 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 coefficients in an elementary fashion.

Item Type:	Article
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory
Divisions:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders:	University of Kent (https://ror.org/00xkeyj56)
Depositing User:	Rowena Paget
Date Deposited:	05 Sep 2023 11:28 UTC
Last Modified:	06 Sep 2023 09:23 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/102689 (The current URI for this page, for reference purposes)

University of Kent Author Information

Paget, Rowena.

Creator's ORCID:	https://orcid.org/0000-0001-8088-4421
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