English

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

Representation Theory 2022-04-18 v4 Group Theory

Abstract

In this paper the authors provide a complete answer to Donkin's Tilting Module Conjecture for all rank 22 semisimple algebraic groups and SL4(k)\text{SL}_{4}(k) where kk is an algebraically closed field of characteristic p>0p>0. In the process, new techniques are introduced involving the existence of (p,r)(p,r)-filtrations, Lusztig's character formula, and the GrG_{r}T-radical series for baby Verma modules.

Keywords

Cite

@article{arxiv.2103.14164,
  title  = {On Donkin's Tilting Module Conjecture I: Lowering the Prime},
  author = {Christopher P. Bendel and Daniel K. Nakano and Cornelius Pillen and Paul Sobaje},
  journal= {arXiv preprint arXiv:2103.14164},
  year   = {2022}
}
R2 v1 2026-06-24T00:34:20.097Z