
Journal of Lie Theory 23 (2013), No. 3, 691697 Copyright Heldermann Verlag 2013 A Remark on Pillen's Theorem for Projective Indecomposable kG(n)Modules Yutaka Yoshii National College of Technology, 22 Yata, Yamatokoriyama, Nara, Japan 6391080 yyoshii@libe.narak.ac.jp [Abstractpdf] 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 $3(h1)$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 $2(h1)$deep. Keywords: Loewy series, projective indecomposable modules, 2(h1)deep weights MSC: 20C33, 20G05, 20G15 [ Fulltextpdf (244 KB)] for subscribers only. 