Counterexamples to the Tilting and $(p,r)$-Filtration Conjectures
Representation Theory
2019-02-20 v2
Abstract
In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic 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 -Weyl filtration. This answers an old question of Jantzen, and also provides a counterexample to the -Filtration Conjecture.
Keywords
Cite
@article{arxiv.1901.06687,
title = {Counterexamples to the Tilting and $(p,r)$-Filtration Conjectures},
author = {Christopher P. Bendel and Daniel K. Nakano and Cornelius Pillen and Paul Sobaje},
journal= {arXiv preprint arXiv:1901.06687},
year = {2019}
}