Irreducible characters of 3′-degree of finite symmetric, general linear and unitary groups

Eugenio Giannelli; Joan Tent; Pham Huu Tiep

doi:10.1016/j.jpaa.2017.09.006

Irreducible characters of 3′-degree of finite symmetric, general linear and unitary groups

Eugenio Giannelli, Joan Tent, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let G be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to 3. We construct a canonical correspondence between irreducible characters of degree coprime to 3 of G and those of N_G(P), where P is a Sylow 3-subgroup of G. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that fields of values of character correspondents are the same.

Original language	English (US)
Pages (from-to)	2199-2228
Number of pages	30
Journal	Journal of Pure and Applied Algebra
Volume	222
Issue number	8
DOIs	https://doi.org/10.1016/j.jpaa.2017.09.006
State	Published - Aug 2018

ASJC Scopus subject areas

Algebra and Number Theory

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abstract = "Let G be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to 3. We construct a canonical correspondence between irreducible characters of degree coprime to 3 of G and those of NG(P), where P is a Sylow 3-subgroup of G. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that fields of values of character correspondents are the same.",

author = "Eugenio Giannelli and Joan Tent and Tiep, {Pham Huu}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

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AU - Giannelli, Eugenio

AU - Tent, Joan

AU - Tiep, Pham Huu

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N2 - Let G be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to 3. We construct a canonical correspondence between irreducible characters of degree coprime to 3 of G and those of NG(P), where P is a Sylow 3-subgroup of G. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that fields of values of character correspondents are the same.

AB - Let G be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to 3. We construct a canonical correspondence between irreducible characters of degree coprime to 3 of G and those of NG(P), where P is a Sylow 3-subgroup of G. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that fields of values of character correspondents are the same.

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ER -

Irreducible characters of 3′-degree of finite symmetric, general linear and unitary groups

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