Journal of group theory: Action of automorphisms on irreducible characters of finite reductive groups of type

Bibliografische Daten

cmsPage: Berolinensien

Zugriffsbeschränkung

Nutzungslizenz

Der Status des Urheberrechts und der verwandten Schutzrechte für diesen Datensatz wurde nicht geprüft oder ist unklar. Bitte wenden Sie sich für weitere Informationen an die Organisation, die das Objekt zur Verfügung gestellt hat.

Titel:: Action of automorphisms on irreducible characters of finite reductive groups of type

Zusammenfassung:: Abstract: Let be a finite reductive group such that the derived subgroup of the underlying algebraic group is a product of quasi-simple groups of type. In this paper, we give an explicit description of the action of automorphisms of on the set of its irreducible complex characters. This generalizes a recent result of M. Cabanes and B. Späth [Equivariant character correspondences and inductive McKay condition for type, J. Reine Angew. Math. 728 (2017), 153–194] and provides a useful tool for investigating the local sides of the local-global conjectures as one usually needs to deal with Levi subgroups. As an application we obtain a generalization of the stabilizer condition in the so-called inductive McKay condition [B. Späth, Inductive McKay condition in defining characteristic, Bull. Lond. Math. Soc. 44 (2012), 3, 426–438; Theorem 2.12] for irreducible characters of. Moreover, a criterion is given to explicitly determine whether an irreducible character is a constituent of a given generalized Gelfand–Graev character of.