Geodesic
A Remark on Pillen's Theorem for Projective Indecomposable kG(n)-Modules
Journal of Lie theory, Tome 23 (2013) no. 3, pp. 691-697.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let $g$ be a connected, semisimple and simply connected algebraic group defined and split over the finite field of order $p$, and let $g(n)$ be the corresponding finite chevalley group and $g_n$ the $n$-th frobenius kernel. Pillen has proved that for a $3(h-1)$-deep and $p^n$-restricted weight $\lambda$, the $G$-module $Q_n(\lambda)$ which is extended from the $G_n$-PIM for $\lambda$ has the same socle series as the corresponding $kG(n)$-PIM $U_n(\lambda)$. Here we remark that this fact already holds for $\lambda$ being $2(h-1)$-deep.
Classification : 20C33, 20G05, 20G15
Mots-clés : Loewy series, projective indecomposable modules, 2(h-1)-deep weights 
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     author = {Y. Yoshii },
     title = {A {Remark} on {Pillen's} {Theorem} for {Projective} {Indecomposable} {kG(n)-Modules}},
     journal = {Journal of Lie theory},
     pages = {691--697},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_3_JLT_2013_23_3_a4/}
}
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Y. Yoshii . A Remark on Pillen's Theorem for Projective Indecomposable kG(n)-Modules. Journal of Lie theory, Tome 23 (2013) no. 3, pp. 691-697. http://geodesic.mathdoc.fr/item/JLT_2013_23_3_JLT_2013_23_3_a4/