### Abstract

Let q be an odd prime power, n > 1, and let P denote a maximal parabolic subgroup of GL_{n} (q) with Levi subgroup GL_{n-1} (q) × GL_{1} (q). We restrict the odd-degree irreducible characters of GL_{n} (q) to P to discover a natural correspondence of characters, both for GL_{n} (q) and SL_{n} (q). A similar result is established for certain finite groups with self-normalizing Sylow p-subgroups. Next, we construct a canonical bijection between the odd-degree irreducible characters of G = S_{n}, GL_{n} (q) or GU_{n} (q) with q odd, and those of N_{G}(P), where P is a Sylow 2-subgroup of G. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that the fields of values of character correspondents are the same. We use this to answer some questions of R. Gow.

Original language | English (US) |
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Pages (from-to) | 6089-6118 |

Number of pages | 30 |

Journal | International Mathematics Research Notices |

Volume | 2017 |

Issue number | 20 |

DOIs | |

State | Published - Oct 1 2017 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*International Mathematics Research Notices*,

*2017*(20), 6089-6118. https://doi.org/10.1093/imrn/rnw174