On Donkin's Tilting Module Conjecture II: Counterexamples

2021/07/24 by Christopher P. Bendel, Bendel, Christopher P., Daniel K. Nakano +5 · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #Advanced Algebra and Geometry #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2107.11615

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 \rmA_n or \rmB₂.

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• Tilting modules for reductive algebraic groups: characters and support varieties

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