2009/09/11 by Doty, S. R.
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.0909.2239
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.