Journal of Lie Theory

no. 3
Factoring Tilting Modules for Algebraic Groups
Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 531-535
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.
DOI: 10.5802/jolt.567
Classification: 20G15, 20G05
Keywords: Tilting modules, tensor products 
@article{JOLT_2009_19_3_a5,
     author = {S. R. Doty},
     title = {Factoring {Tilting} {Modules} for {Algebraic} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {531--535},
     year = {2009},
     volume = {19},
     number = {3},
     doi = {10.5802/jolt.567},
     zbl = {1182.20040},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.567/}
}
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S. R. Doty. Factoring Tilting Modules for Algebraic Groups. Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 531-535. doi: 10.5802/jolt.567

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