Invariant lattices in the Steinberg module and their isometry groups
Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 519-529 Cet article a éte moissonné depuis la source Math-Net.Ru

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The main goal of this paper is the investigation of invariant lattices and the computation of their isometry groups when $G=\operatorname{SL}(2,q)$ and $V$ is the Steinberg module.
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     title = {Invariant lattices in {the~Steinberg} module and their isometry groups},
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V. P. Burichenko. Invariant lattices in the Steinberg module and their isometry groups. Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 519-529. http://geodesic.mathdoc.fr/item/SM_1995_80_2_a13/

[1] Kertis Ch., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 | MR

[2] Plesken W., “Finite unimodular groups of prime degree and circulants”, J. Algebra, 97 (1985), 286–312 | DOI | MR | Zbl

[3] Plesken W., Group Rings of Finite Groups Over p-adic Integers, Lect. Notes in Math., 1026, 1983 | MR | Zbl

[4] Konvei Dzh., Sloen N., Upakovki sharov, reshetki i gruppy, Mir, M., 1989

[5] Kameron P., van Lint Dzh., Teoriya grafov, teoriya kodirovaniya i blok-skhemy, Nauka, M., 1980 | MR

[6] van Lint J. H., MacWilliams F. J., “Gneneralized qudratic residue codes”, IEEE Trans. in Information Theory, 24:6 (1978), 730–737 | DOI | MR | Zbl

[7] Ward H. N., “Quadratic residue codes and symplectic groups”, J. Algebra, 29 (1974), 150–171 | DOI | MR | Zbl

[8] Kostrikin A. I., Kostrikin I. A., Ufnarovskii V. A., “Invariantnye reshetki tipa $G_2$ i ikh gruppy avtomorfizmov”, Tr. MIAN, 165, Nauka, M., 1984, 79–97 | MR | Zbl

[9] Bondal A. I., Kostrikin A. I., Fam Khyu Tep, “Invariantnye reshetki, reshetka Licha i ee setnye unimodulyarnye analogi v algebrakh $A_{p-1}$”, Matem sb., 130(172) (1986), 435–464 | MR | Zbl

[10] Gorenstein D., Finite Groups, Harper and Row, N.Y., 1968 | MR | Zbl

[11] Ivanov D. N., “Ortogonalnye razlozheniya algebr Li tipa $A_{p^n-1}$ i $D_n$ s konechnym chislom klassov podobnykh invariantnykh podreshetok”, Vestn. MGU. Ser. 1. Matematika, mekhanika, 1989, no. 2, 40–43 | Zbl

[12] Coxeter H. S. M., “Extreme forms”, Canad. J. Math., 3 (1951), 391–441 | MR | Zbl

[13] Thompson J. G., “A simple subgroup of $E_8(3)$”, Finite groups, Simp. Japan Soc. for Promotion of Science, 1976, 113–116

[14] Plesken W., Pohst M., “On maxmal finite irreducible subgroups of $\operatorname {GL}(n,\mathbb Z)$”, Math. Comp., 31 (1977), 536–577 ; Math. Comp., 34 (1980), 245–301 | DOI | MR | DOI | MR

[15] Kameron P. Dzh., “Konechnye gruppy podstanovok i konechnye prostye gruppy”, UMN, 38:3 (1983), 135–158 | MR