On Donkin's Tilting Module Conjecture II: Counterexamples

TL;DR

This paper constructs infinite families of counterexamples to longstanding conjectures in representation theory of algebraic groups, challenging previous assumptions about Weyl filtrations and tilting modules.

Contribution

It introduces new techniques to explicitly produce counterexamples to Donkin's Tilting Module Conjecture and Jantzen's question, especially in large rank cases.

Findings

Counterexamples exist for all types except A_n and B_2

Methods to generate counterexamples from small to large rank

Explicit constructions of counterexamples in various group types

Abstract

In this paper we produce infinite families of counterexamples to Jantzen's question posed in 1980 on the existence of Weyl $p$-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 $\rm{A}_{n}$ or $\rm{B}_{2}$.