Integral lattices associated with a finite affine group
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 431-443 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper deals with positive definite integral lattices of dimension $\operatorname{Card}(V)-1$ associated with a finite affine group $V\cdot\operatorname{GL}(V)$ (and some of its subgroups). The invariant sublattices are described to within similarity. Duality in the class of invariant lattices is studied. The unimodular lattices are distinguished.
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     title = {Integral lattices associated with a~finite affine group},
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K. S. Abdukhalikov. Integral lattices associated with a finite affine group. Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 431-443. http://geodesic.mathdoc.fr/item/SM_1995_83_2_a8/

[1] Abdukhalikov K. S., “Tselochislennye invariantnye reshetki v algebrakh Li tipa $A_{p^m-1}$”, Matem. sb., 184:4 (1993), 61–104 | MR | Zbl

[2] Algebraicheskaya teoriya chisel, eds. Dzh. Kassels, A. Frelikh, Mir, M., 1969 | MR

[3] Bondal A. I., Kostrikin A. I., Fam Khyu Tep, “Invariantnye reshetki, reshetka Licha i ee chetnye unimodulyarnye analogi v algebrakh Li tipa $A_{p-1}$”, Matem. sb., 130:4 (1986), 435–464 | MR | Zbl

[4] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1985 | MR | Zbl

[5] 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. Matem., mekh., 2 (1989), 40–43 | MR | Zbl

[6] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1985

[7] Fam Khyu Tep, “Predstavleniya Veilya konechnykh simplekticheskikh grupp i reshetki Gou”, Matem. sb., 182:8 (1991), 1177–1199

[8] Fam Khyu Tep, “Bazisnye spinornye predstavleniya znakoperemennykh grupp, reshetki Gou i reshetki Barnsa–Uolla”, Matem. sb., 183:11 (1992), 99–116

[9] Conway J. H., Sloane N. J. A., Sphere packings, lattices and groups, Springer, Grundlehren, 1988 | MR

[10] Conway J. H., Sloane N. J. A., “A new upper bound for the minimum of an integral lattices of determinant, 1”, Bull. Amer. Math. Soc., 23 (1990), 383–387 | DOI | MR | Zbl

[11] Gow R., “Even unimodular lattices associated with the Weil representations of finite symplectic group”, J. Algebra, 122 (1989), 510–519 | DOI | MR | Zbl

[12] Gross B. H., “Group representations and lattices”, J. Amer. Math. Soc., 3 (1990), 929–960 | DOI | MR | Zbl