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arXiv · 2412.05703

The $p$-rationality of height-zero characters

Nguyen N. Hung·A. A. Schaeffer Fry
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Abstract

We propose and present evidence for a conjectural global-local phenomenon concerning the $p$-rationality of $p$-height-zero characters. Specifically, if $\chi$ is a height-zero character of a finite group $G$ and $D$ is a defect group of the $p$-block of $G$ containing $\chi$, then the $p$-rationality of $\chi$ can be captured inside the normalizer $N_G(D)$.

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BibTeXRIS

Nguyen N. Hung, A. A. Schaeffer Fry. 2024-12-07. The $p$-rationality of height-zero characters. https://arxiv.org/abs/2412.05703

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