Journal of Lie Theory

no. 3
A Remark on Pillen's Theorem for Projective Indecomposable kG(n)-Modules
Journal of Lie Theory, Volume 23 (2013) no. 3, pp. 691-697
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.
DOI: 10.5802/jolt.744
Classification: 20C33, 20G05, 20G15
Keywords: Loewy series, projective indecomposable modules, 2(h-1)-deep weights 
@article{JOLT_2013_23_3_a4,
     author = {Y. Yoshii},
     title = {A {Remark} on {Pillen's} {Theorem} for {Projective} {Indecomposable} {kG(n)-Modules}},
     journal = {Journal of Lie Theory},
     pages = {691--697},
     year = {2013},
     volume = {23},
     number = {3},
     doi = {10.5802/jolt.744},
     zbl = {1279.20020},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.744/}
}
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Y. Yoshii. A Remark on Pillen's Theorem for Projective Indecomposable kG(n)-Modules. Journal of Lie Theory, Volume 23 (2013) no. 3, pp. 691-697. doi: 10.5802/jolt.744

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