On Donkin's Tilting Module Conjecture II: Counterexamples
Representation Theory
2023-11-14 v3 Group Theory
Abstract
In this paper we produce infinite families of counterexamples to Jantzen's question posed in 1980 on the existence of Weyl -filtrations for Weyl modules for an algebraic group and Donkin's Tilting Module Conjecture formulated in 1990. New techniques to exhibit explicit examples are provided along with methods to produce counterexamples in large rank from counterexamples in small rank. Counterexamples can be produced via our methods for all groups other than when the root system is of type or .
Cite
@article{arxiv.2107.11615,
title = {On Donkin's Tilting Module Conjecture II: Counterexamples},
author = {Christopher P. Bendel and Daniel K. Nakano and Cornelius Pillen and Paul Sobaje},
journal= {arXiv preprint arXiv:2107.11615},
year = {2023}
}