On the representations of reductive groups with disconnected centre. (English) Zbl 0703.20036

Orbites unipotentes et représentations. I. Groupes finis et algèbres de Hecke, Astérisque 168, 157-166 (1988).
[For the entire collection see Zbl 0695.00014.]
Let \(G\) be a connected reductive algebraic group defined over a finite field \({\mathbb{F}}_ q\) with Frobenius map \(F:G\to G\). In the case where the center \(Z_ G\) of \(G\) is connected, a parametrization for the set \(G^ F\) of irreducible representations up to isomorphism of the finite group \(G^ F\) over \(\overline Q_{\ell}\) (\(\ell\) is a prime not dividing \(q\)) was given by the author [Characters of reductive groups over a finite field (Ann. Math. Stud. 107, 1984; Zbl 0556.20033)]. In the paper under review this is extended to the general case (i.e. \(Z_ G\) is allowed to be disconnected).
Reviewer: V.L.Popov


20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields