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.
Original language | English |
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Pages (from-to) | 321-357 |
Number of pages | 37 |
Journal | Algebraic Combinatorics |
Volume | 6 |
Issue number | 2 |
DOIs | |
Publication status | Published - 3 May 2023 |
Keywords
- character deflation
- plethysm
- Sylow branching coefficients