Geodesic
Representations of the full linear group over a finite field
Sbornik. Mathematics, Tome 12 (1970) no. 1, pp. 13-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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S. I. Gel'fand. Representations of the full linear group over a finite field. Sbornik. Mathematics, Tome 12 (1970) no. 1, pp. 13-39. http://geodesic.mathdoc.fr/item/SM_1970_12_1_a1/

[1] Z. I. Borevich, I. R. Shafarevich, Teoriya chisel, Nauka, Moskva, 1964 | MR

[2] I. M. Gelfand, M. I. Graev, “Kategorii predstavlenii grupp i zadacha o klassifikatsii neprivodimykh predstavlenii”, DAN SSSR, 146:4 (1962), 757–760 | MR

[3] I. M. Gelfand, M. I. Graev, “Konstruktsiya neprivodimykh predstavlenii prostykh algebraicheskikh grupp nad konechnym polem”, DAN SSSR, 147:3 (1962), 620–632 | MR

[4] I. M. Gelfand, M. A. Naimark, Unitarnye predstavleniya klassicheskikh grupp, Trudy matem. in-ta im. V. A. Steklova, 36, 1950 | MR | Zbl

[5] I. M. Gelfand, I. I. Pyatetskii-Shapiro, “Teoriya predstavlenii i teoriya avtomorfnykh funktsii”, Uspekhi matem. nauk, XIV:2(86) (1959), 171–194

[6] S. I. Gelfand, “Analiticheskie predstavleniya polnoi lineinoi gruppy nad konechnym polem”, DAN SSSR, 182:2 (1968), 251–254 | MR

[7] S. I. Gelfand, “O neprivodimykh mnogochlenakh nad konechnym polem”, Uspekhi matem. nauk, XXIV:4(148) (1969), 193–194. | MR

[8] A. A. Kirillov, “Predstavleniya polnoi matrichnoi gruppy”, DAN SSSR, 144:1 (1962), 37–39 | MR | Zbl

[9] G. Makki, “Beskonechnomernye predstavleniya grupp”, Matematika, 6:6 (1962), 57–103

[10] G. Frobenius, Teoriya kharakterov i predstavlenii grupp, Kharkov, 1937

[11] F. Bruhat, “Sur les representations induites des groupes de Lie”, Bull. Soc. Math. France, 84 (1956), 97–205 | MR | Zbl

[12] L. E. Dickson, Linear groups, New York, 1958

[13] J. A. Green, “The characters of the finite general linear groups”, Trans. Amer. Math. Soc., 80 (1955), 402–447 | DOI | MR | Zbl

[14] Harish-Chandra, “Two theorems on a semisimple groups”, Ann. Math., 83 (1966), 73–128 | DOI | MR

[15] Harish-Chandra, “Automorphic forms on semisimple Lie groups”, Lecture Notes Math., 62 (1968) | MR

[16] Harish-Chandra, Eisenstein series over finite fields, Preprint, 1968

[17] K. P. Parthasarathy, R. R. Rao, V. S. Varadarajan, “Representations of the complex semisimple Lie groups and Lie algebras”, Ann. Math., 85 (1967), 383–429 | DOI | MR | Zbl

[18] I. Schur, “Untersuchungen über die Darstellungen der endlichen Gruppen durch Gebrochene lineare Substitutionen”, J. für Math., 132 (1907), 85 | Zbl

[19] R. Steinberg, “The representations of $GL(3,q)$, $PGL(3,q)$, $GL(4,q)$ and $PGL(4,q)$”, Canad. J. Math, 3 (1951), 225–235 | MR | Zbl

[20] R. Steinberg, “A geometric approach to the representations of the full linear group over a Galois field”, Trans. Amer. Math. Soc., 74 (1951), 274–282 | DOI | MR

[21] S. Tanaka, “Construction and classification of irreducible representations of special linear group of second order over finite field”, Osaka Math. J., 4 (1968), 65–84