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The Representations of GL(3,q), GL(4,q), PGL(3,q), and PGL(4,q)

Published online by Cambridge University Press:  20 November 2018

Robert Steinberg
Affiliation:
University of California at Los Angeles
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Extract

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 the related groups, SL(n, q), PGL(n, q), PSL(n, q), the corresponding group of determinant unity, projective group, projective group of determinant unity, respectively.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1951

References

[1] Brinkmann, H. W., Bull. Amer. Math. Soc, vol. 27 (1921), 152.Google Scholar
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[3] Frobenius, G., Über Gruppencharaktere, Berliner Sitz. (1896), 985.Google Scholar
[4] Frobenius, G., Über die Darstellung der endlichen Gruppen durch Lineare Substitutionen, Berliner Sitz. (1897), 994.Google Scholar
[5] Frobenius, G., Über Relationen zwischen den Charakteren einer Gruppe und denen ihrer Untergruppen, Berliner Sitz. (1898), 501.Google Scholar
[6] Jordan, H., Group-Characters of Various Types of Linear Groups, Amer. J. of Math., vol. 29 (1907), 387.CrossRefGoogle Scholar
[7] Schur, I., Untersuchungen ûber die Darstellung der endlichen Gruppen durch Gebrochene Lineare Substitutionen, J. fur Math., vol. 132 (1907), 85.Google Scholar
[8] Speiser, A., Die Théorie der Gruppen von endlicher Ordnung (Berlin, 1937).Google Scholar
[9] Steinberg, R., A Geometric Approach to the Representations of Hie Full Linear Group over a Galois Field, submitted to Trans. Amer. Math. Soc. Google Scholar
[10] Steinberg, R., Representations on the Linear Fractional Groups, Thesis, University of Toronto Library. Google Scholar

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