## Characters of reductive groups over finite fields.(English)Zbl 0572.20026

Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, 877-880 (1984).
[For the entire collection see Zbl 0553.00001.]
Let G be a connected reductive algebraic group defined over a finite field $$F_ q$$ and $$G(F_ q)$$ the finite group of $$F_ q$$-rational points of G. In his book [Characters of reductive groups over a finite field, Ann. Math. Stud. 107 (1984; Zbl 0556.20033)] the author gave a classification of the (complex) irreducible representations of $$G(F_ q)$$ under the assumption that the center of G is connected. Here the author states that this assumption can be dropped and describes the classification. The description here is more in the spirit of Chapter 13 of [loc. cit.] rather than that of the Main Theorem 7.23; and the Langlands dual H of G over $${\mathbb{C}}$$ is used, rather than a dual group $$G^*$$ over $$F_ q$$. The parameterization of the irreducible representations is in terms of certain finite sets $$\bar {\mathcal M}(g)$$ associated with ”special” elements g in H.
Reviewer: B.Srinivasan

### MSC:

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

### Citations:

Zbl 0553.00001; Zbl 0556.20033