Galois Automorphisms and Classical Groups

Jay Taylor, A. A. Schaeffer Fry

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Abstract

In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the finite symplectic groups. We generalise this in two directions. Firstly, using work of the first-named author, we give a complete description of the action of the Galois group on irreducible characters. Secondly, we extend both descriptions to cover the case of special orthogonal groups. As a consequence, we obtain explicit descriptions for the character fields of symplectic and special orthogonal groups.
Original languageEnglish
JournalTransformation Groups
Volume28
Issue number1
Early online date29 Jul 2022
DOIs
Publication statusPublished - 1 Mar 2023

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