On plethysms and Sylow branching coefficients

Stacey Law; Yuji Okitani

doi:10.5802/alco.262

On plethysms and Sylow branching coefficients

Stacey Law, Yuji Okitani

Mathematics

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Abstract

We prove a recursive formula for plethysm coefficients of the form a^μ_λ,(m), generalising 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.

Original language	English
Pages (from-to)	321-357
Number of pages	37
Journal	Algebraic Combinatorics
Volume	6
Issue number	2
DOIs	https://doi.org/10.5802/alco.262
Publication status	Published - 3 May 2023

Keywords

character deflation
plethysm
Sylow branching coefficients

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title = "On plethysms and Sylow branching coefficients",

abstract = "We prove a recursive formula for plethysm coefficients of the form aμλ,(m), generalising 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 Pn denote a Sylow 2-subgroup of Sn, we show that almost all Sylow branching coefficients of Sn corresponding to the trivial character of Pn are positive.",

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T1 - On plethysms and Sylow branching coefficients

AU - Law, Stacey

AU - Okitani, Yuji

PY - 2023/5/3

Y1 - 2023/5/3

N2 - We prove a recursive formula for plethysm coefficients of the form aμλ,(m), generalising 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 Pn denote a Sylow 2-subgroup of Sn, we show that almost all Sylow branching coefficients of Sn corresponding to the trivial character of Pn are positive.

AB - We prove a recursive formula for plethysm coefficients of the form aμλ,(m), generalising 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 Pn denote a Sylow 2-subgroup of Sn, we show that almost all Sylow branching coefficients of Sn corresponding to the trivial character of Pn are positive.

KW - character deflation

KW - plethysm

KW - Sylow branching coefficients

UR - https://arxiv.org/abs/2110.14552

U2 - 10.5802/alco.262

DO - 10.5802/alco.262

M3 - Article

VL - 6

SP - 321

EP - 357

JO - Algebraic Combinatorics

JF - Algebraic Combinatorics

IS - 2

ER -

On plethysms and Sylow branching coefficients

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