Factoring tilting modules for algebraic groups

Details Factoring tilting modules for algebraic groups Factoring tilting modules for algebraic groups

2009-09-11

arxiv.org/abs/0909.2239v1

Mathematics

Representation Theory

6 pages

Scientific paper

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.

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