Computation of the character table of affine groups using Fischer matrices. (English) Zbl 0854.20006
Campbell, C. M. (ed.) et al., Groups ‘93 Galway/St. Andrews’. Proceedings of the international conference, held in Galway, Ireland, August 1-14, 1993. Volume 1. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 211, 131-137 (1995).
[Mostly from the authors’ abstract.] Let \(\text{GL}_n(q)\) be the general linear group and let \(H_n=V_n(q).\text{GL}_n(q)\) denote the affine group of \(V_n(q)\). In this paper the authors compute the character tables for \(n=2,3,4\) using Fischer’s method which is briefly described. Results from B. Fischer [in Representation theory of finite groups and finite dimensional algebras 1991, Prog. Math. 95, 1-16 (1991; Zbl 0804.20003)] and R. J. List [Arch. Math. 51, No. 2, 118-124 (1988; Zbl 0628.20015)] are used to obtain Fischer matrices for the conjugacy classes of \(\text{GL}_n(q)\). It turns out that the groups \(H_2\), \(H_3\), and \(H_4\) have \(q^2+q-1\), \(q^3+q^2-1\), and \(q^4+q^3+q^2-q-1\) irreducible characters.
Note that no complete character tables are given, only the degrees of all irreducible characters are listed in the paper.
For the entire collection see [Zbl 0810.00013].
Note that no complete character tables are given, only the degrees of all irreducible characters are listed in the paper.
For the entire collection see [Zbl 0810.00013].
Reviewer: M.Weller (Essen)
MSC:
| 20C15 | Ordinary representations and characters |
| 20C40 | Computational methods (representations of groups) (MSC2010) |
| 20-04 | Software, source code, etc. for problems pertaining to group theory |
| 20G05 | Representation theory for linear algebraic groups |
| 20G40 | Linear algebraic groups over finite fields |
