The characters of the finite general linear groups

  title={The characters of the finite general linear groups},
  author={J. A. Green},
  journal={Transactions of the American Mathematical Society},
  • 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… 

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