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On Donkin's tilting module conjecture II: counterexamples
Published online by Cambridge University Press: 02 May 2024
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 ${\rm B}_{2}$.
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- © 2024 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence
Footnotes
Research of the first author was supported in part by Simons Foundation Collaboration Grant 317062. Research of the second author was supported in part by NSF grants DMS-1701768 and DMS-2101941. Research of the third author was supported in part by Simons Foundation Collaboration Grant 245236.