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math.RT2017
A new proof of Nakayama's Conjecture via Brauer quotients of Young modules
William O'Donovan
We provide a self-contained proof of the main properties of Brauer quotients of Young modules. We then use these results to give a new inductive proof of Nakayama's Conjecture on t…
math.RT2015
The Action of Generalised Symmetric Groups on Symmetric and Exterior Powers of Their Natural Representations
Bill O'Donovan
We establish upper and lower bounds on the dimension of the space spanned by the symmetric powers of the natural character of generalised symmetric groups. We adapt the methods of…
math.RT2015★ 3 cited
On signed p-Kostka numbers and the indecomposable signed Young permutation modules
Eugenio Giannelli, Kay Jin Lim, William O'Donovan +1
We prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Brou{é} corresponde…