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Mat. Sb. (N.S.), 1970, Volume 83(125), Number 1(9), Pages 15–41 (Mi msb3499)  

This article is cited in 6 scientific papers (total in 6 papers)

Representations of the full linear group over a finite field

S. I. Gel'fand


Abstract: Complex representations of the group $GL(n,\mathbf F_q)$ are studied, where $\mathbf F_q$ is a field of order $q$. The concept of analytic representations of $GL(n,\mathbf F_q)$ is introduced and is used to construct all the irreducible representations of $GL(n,\mathbf F_q)$. Results are obtained on the irreducible polynomials of 3rd degree over $\mathbf F_q$.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Sbornik, 1970, 12:1, 13–39

Bibliographic databases:

UDC: 512.864
MSC: 20G05, 20G40, 20C11, 33C10, 11C08
Received: 23.10.1969

Citation: S. I. Gel'fand, “Representations of the full linear group over a finite field”, Mat. Sb. (N.S.), 83(125):1(9) (1970), 15–41; Math. USSR-Sb., 12:1 (1970), 13–39

Citation in format AMSBIB
\Bibitem{Gel70}
\by S.~I.~Gel'fand
\paper Representations of the full linear group over a~finite field
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 83(125)
\issue 1(9)
\pages 15--41
\mathnet{http://mi.mathnet.ru/msb3499}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=272916}
\zmath{https://zbmath.org/?q=an:0252.20034}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 12
\issue 1
\pages 13--39
\crossref{https://doi.org/10.1070/SM1970v012n01ABEH000907}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. A. Gol'fand, “An exceptional representation of $Sp(4,F_q)$”, Funct. Anal. Appl., 12:4 (1978), 312–314  mathnet  crossref  mathscinet  zmath
    2. S. P. Khekalo, “The Bessel function on a finite field”, Russian Math. (Iz. VUZ), 45:2 (2001), 74–77  mathnet  mathscinet  zmath  elib
    3. Zhengyu Mao, “Spherical Bessel Functions of GL2(Fq2)”, Journal of Number Theory, 87:1 (2001), 154  crossref
    4. I. Tulunay, “Cuspidal Modules as Summands of a Gel'fand–Graev Module”, Communications in Algebra, 32:4 (2004), 1519  crossref
    5. I. Tulunay, “Restriction of a cuspidal module for finite general linear groups”, Journal of Algebra, 273:1 (2004), 60  crossref
    6. E. E. Goryachko, “The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions”, J. Math. Sci. (N. Y.), 141:4 (2007), 1407–1416  mathnet  crossref  mathscinet  zmath  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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