
Journal of Lie Theory 19 (2009), No. 3, 531535 Copyright Heldermann Verlag 2009 Factoring Tilting Modules for Algebraic Groups Stephen R. Doty Dept. of Mathematics and Statistics, Loyola University, Chicago, IL 60626, U.S.A. doty@math.luc.edu Let G be a semisimple, simplyconnected algebraic group over an algebraically closed field of characteristic p > 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting. Although quite easy to prove, this fact does not seem to have been observed before. It has the following consequence: If p ≥ 2h2 and a given tilting module has highest weight padically close to the rth Steinberg weight, then the tilting module is isomorphic to a tensor product of two simple modules, usually in many ways. Keywords: Tilting modules, tensor products. MSC: 20G15; 20G05 [ Fulltextpdf (131 KB)] for subscribers only. 