On Donkin’s tilting module conjecture I: lowering the prime

Bendel, Christopher; Nakano, Daniel; Pillen, Cornelius; Sobaje, Paul

doi:10.1090/ert/608

On Donkin’s tilting module conjecture I: lowering the prime
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by Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen and Paul Sobaje

Represent. Theory 26 (2022), 455-497

DOI: https://doi.org/10.1090/ert/608

Published electronically: April 4, 2022

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Abstract:

In this paper the authors provide a complete answer to Donkin’s Tilting Module Conjecture for all rank $2$ semisimple algebraic groups and $\operatorname {SL}_{4}(k)$ where $k$ is an algebraically closed field of characteristic $p>0$. In the process, new techniques are introduced involving the existence of $(p,r)$-filtrations, Lusztig’s character formula, and the $G_{r}$T-radical series for baby Verma modules.

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