Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen, Paul Sobaje
Published 2021-07-24Version 1
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 $\rm{B}_{2}$.
On Donkin's Tilting Module Conjecture I: Lowering the Prime
On Donkin's Tilting Module Conjecture III: New Generic Lower Bounds
On integral $\mathrm{Ext^2}$ between certain Weyl modules of $\mathrm{GLn}$
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