# The characters of the finite general linear groups

```@article{Green1955TheCO,
title={The characters of the finite general linear groups},
author={J. A. Green},
journal={Transactions of the American Mathematical Society},
year={1955},
volume={80},
pages={402-447}
}```
• J. Green
• Published 1 February 1955
• Mathematics
• Transactions of the American Mathematical Society
Introduction. In this paper we show how to calculate the irreducible characters of the group GL(n, q) of all nonsingular matrices of degree n with coefficients in the finite field of q elements. These characters have been given for n = 2 by H. Jordan [8], Schur [10], and others, and for n =3 and n =4 by Steinberg [12], who has also [13] done important work in the general case. We are concerned here with "ordinary" characters, that is, characters of representations by matrices with complex…
515 Citations
• Mathematics
• 2000
Let k be a finite field, k Ik the degree n extension of k, and G = GLn(k) the general linear group with entries in k. This paper studies the "generalized Steinberg" (GS) representationis of G and
Let k be a finite field, and k2 the quadratic extension of k. The purpose of the present paper is to announce a theorem which gives a method to construct the irreducible characters of the finite
• S. Donkin
• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 1993
The ring of symmetric polynomials in n variables may be interpreted as a ring of characters of the general linear group GL(n) (see e.g. [4], §3·5). We consider here a generalization of symmetric
• Mathematics
• 1998
Throughout this paper, r will denote a prime. Our object in this paper and another is to describe the finite irreducible subgroups of L(r):=SL(r, C), where C denotes the field of complex numbers. The
The purpose of the present paper is to give some results concerning (complex) characters and unipotent elements of finite Chevelley groups. Main results are proved by two simple lemmas stated in
• Mathematics
• 1989
Introduction. In this note we announce some results on the character theory of the finite unitary groups. The main result is the decomposition of the restriction of a certain class function / t o a
In this note we present a construction for a distinguished representation in the discrete series of GLn(F), F a finite field. This is used in describing explicitly Brauer's lifting of the identity
Let q be a prime power, C = GLsw ( q ) and let r be a prime not dividing q. Using representations of Hecke algebras associated with symmetric groups over arbitrary fields, the r-modular irreducible
The representation theory of a group G over the field of complex numbers involves two problems: first, the construction of the irreducible representations of G; and second, the problem of expressing

## References

SHOWING 1-9 OF 9 REFERENCES

Let (5 be a group of finite order g. By a generalized character of (M, we shall mean a linear combination of the (ordinary) irreducible characters of (M with integral rational coefficients. The main
This paper is a result of an investigation into general methods of determining the irreducible characters of GL(n, q), the group of all non-singular linear substitutions with marks in GF(q), and of

### Uber Relationen zwischen den Charakteren einer Gruppe und denen ihrer Untergruppen

• Uber die Komposition der Charaklere einer Gruppe

• 1937