Abstract
In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic p that is not the restriction of an indecomposable tilting module. This yields a counterexample to Donkin’s longstanding Tilting Module Conjecture. The authors also produce a Weyl module that does not admit a p-Weyl filtration. This answers an old question of Jantzen, and also provides a counterexample to the
In memory of Elena Galaktionova
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1701768
Funding source: Simons Foundation
Award Identifier / Grant number: 317062
Award Identifier / Grant number: 245236
Funding statement: Research of the first author was supported in part by Simons Foundation Collaboration Grant 317062. Research of the second author was supported in part by NSF grant DMS-1701768. Research of the third author was supported in part by Simons Foundation Collaboration Grant 245236.
Acknowledgements
The authors would like to thank Henning H. Andersen, Jens C. Jantzen, and also the referees of this paper for many helpful comments and suggestions.
References
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