On $\boldsymbol{p}$-rationality in double covers of symmetric and alternating groups

Olivier Brunat; Rishi Nath

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arXiv · 2609.15244

On $\boldsymbol{p}$-rationality in double covers of symmetric and alternating groups

Olivier Brunat·Rishi Nath

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Abstract

We construct, for every odd prime $p$, a bijection between the $p'$-spin characters $\widetilde S_n$ and those of a Sylow normalizer which, in particular, is equivariant under the Galois action detecting $p$-rationality. An analogous result holds for $\widetilde A_n$. We also obtain a blockwise refinement for height-zero spin characters and their Brauer correspondents.

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BibTeX RIS

Olivier Brunat, Rishi Nath. 2026-09-14. On $\boldsymbol{p}$-rationality in double covers of symmetric and alternating groups. https://arxiv.org/abs/2609.15244

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