Geodesic
On plethysms and Sylow branching coefficients
Law, Stacey1 ; Okitani, Yuji2
1 Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge CB3 0WB UK
2 Department of Mathematics University of California Berkeley CA 94720 USA
Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 321-357

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We prove a recursive formula for plethysm coefficients of the form a λ,(m) μ , encompassing those which arise in a long-standing conjecture of Foulkes. This also generalises results on plethysms due to Bruns–Conca–Varbaro and de Boeck–Paget–Wildon. From this we deduce a stability result and resolve two conjectures of de Boeck concerning plethysms, as well as obtain new results on Sylow branching coefficients for symmetric groups for the prime 2. Further, letting P n denote a Sylow 2-subgroup of S n , we show that almost all Sylow branching coefficients of S n corresponding to the trivial character of P n are positive.

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DOI : 10.5802/alco.262
Classification : 20C15, 20C30
Keywords: character deflation, plethysm, Sylow branching coefficients

Law, Stacey 1 ; Okitani, Yuji 2

1 Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge CB3 0WB UK
2 Department of Mathematics University of California Berkeley CA 94720 USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Law, Stacey; Okitani, Yuji. On plethysms and Sylow branching coefficients. Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 321-357. doi: 10.5802/alco.262

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