On Donkin's Tilting Module Conjecture I: Lowering the Prime

Christopher P. Bendel; Daniel K. Nakano; Cornelius Pillen; Paul Sobaje

paper

On Donkin's Tilting Module Conjecture I: Lowering the Prime

arXiv:2103.14164

Abstract

In this paper the authors provide a complete answer to Donkin's Tilting Module Conjecture for all rank $2$ semisimple algebraic groups and $SL_{4} (k)$ 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.