arXiv
Open Access
2021
On plethysms and Sylow branching coefficients
Stacey Law
Yuji Okitani
Abstrak
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.
Penulis (2)
S
Stacey Law
Y
Yuji Okitani
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
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- en
- Sumber Database
- arXiv
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- Open Access ✓