Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Computing the irreducible characters of the group $ {\rm GL}\sb 6(2)$


Author: M. R. Darafsheh
Journal: Math. Comp. 46 (1986), 301-319
MSC: Primary 20C15; Secondary 20C30
DOI: https://doi.org/10.1090/S0025-5718-1986-0815851-X
MathSciNet review: 815851
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: All the sixty ordinary irreducible characters of the group of six by six nonsingular matrices over a field with two elements are found. To do this we use methods of Steinberg and also characters induced from certain subgroups which makes it possible to calculate the whole character table by hand.


References [Enhancements On Off] (What's this?)

  • [1] R. Brauer, "On groups whose order contains a prime number to the first power. I," Amer. J. Math., v. 64, 1942, pp. 401-420. MR 0006537 (4:1e)
  • [2] L. E. Dickson, Linear Groups With an Exposition of the Galois Field Theory, Dover, New York, 1958. MR 0104735 (21:3488)
  • [3] I. Martin Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976. MR 0460423 (57:417)
  • [4] D. E. Littlewood, The Theory of Group Characters, Oxford Univ. Press, Oxford, 1958.
  • [5] R. Steinberg, "The representations of $ {\text{GL}}(3,q)$, $ {\text{GL}}(4,q)$, $ {\text{PGL}}(3,q)$ and $ {\text{PGL}}(4,q)$," Canad. J. Math., v. 3, 1951, pp. 225-235. MR 0041851 (13:10e)
  • [6] R. Steinberg, "A geometric approach to the representations of the full linear group over a Galois field," Trans. Amer. Math. Soc., v. 71, 1951, pp. 274-282. MR 0043784 (13:317d)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 20C15, 20C30

Retrieve articles in all journals with MSC: 20C15, 20C30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1986-0815851-X
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society