Journal of Lie Theory 19 (2009), No. 3, 531--535
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, simply-connected 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 ≥ 2h-2 and a given tilting module has highest weight p-adically close to the r-th 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
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