On Donkin's Tilting Module Conjecture II: Counterexamples

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 An or B2.

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“…The results in (1), ( 2) and ( 3 [7] and [8], show that there are exceptions. In a very recent preprint [9] these authors show that the bound on p can in general be lowered to 2h − 4.…”