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arXiv · 2506.04773

On the local representation theory of symmetric groups

Greta Tendi
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Abstract

Given a Sylow $p$-subgroup $P$ of a symmetric group, we describe the action of its normalizer on $\mathrm{Irr}(P)$. To this end, we establish a one-to-one correspondence between the irreducible characters of $P$ and certain equivalence classes of explicitly defined functions, which are also naturally suited to describing the Galois action.

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Greta Tendi. 2025-06-05. On the local representation theory of symmetric groups. https://arxiv.org/abs/2506.04773

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