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On p-rationality in double covers of symmetric and alternating groups
Abstract
We construct, for every odd prime p, a bijection between the p'-spin characters S̃n and those of a Sylow normalizer which, in particular, is equivariant under the Galois action detecting p-rationality. An analogous result holds for Ãn. We also obtain a blockwise refinement for height-zero spin characters and their Brauer correspondents.
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BibTeX
@misc{brunat2026prationality,
title = {{On $\boldsymbolp$-rationality in double covers of symmetric and alternating groups}},
author = {Olivier Brunat and Rishi Nath},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15244},
eprint = {2609.15244},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15244},
}
RIS
TY - UNPB
TI - On p-rationality in double covers of symmetric and alternating groups
AU - Olivier Brunat
AU - Rishi Nath
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15244
UR - https://arxiv.org/abs/2609.15244
AB - We construct, for every odd prime p, a bijection between the p'-spin characters S̃_n and those of a Sylow normalizer which, in particular, is equivariant under the Galois action detecting p-rationality. An analogous result holds for Ã_n. We also obtain a blockwise refinement for height-zero spin characters and their Brauer correspondents.
ER -