On Donkin's tilting module conjecture II: Counterexamples

Christopher P. Bendel; Daniel K. Nakano; Cornelius Pillen; Paul Sobaje

doi:10.1112/S0010437X24007115

On Donkin's tilting module conjecture II: Counterexamples

Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen, Paul Sobaje

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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Abstract

In this paper we produce infinite families of counterexamples to Jantzen's question posed in 1980 on the existence of Weyl -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 or.

Original language	English
Pages (from-to)	1167-1193
Number of pages	27
Journal	Compositio Mathematica
Volume	160
Issue number	6
DOIs	https://doi.org/10.1112/S0010437X24007115
State	Published - May 2 2024

Keywords

algebraic groups
representation theory
tilting modules

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10.1112/S0010437X24007115

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AU - Nakano, Daniel K.

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AU - Sobaje, Paul

PY - 2024/5/2

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N2 - In this paper we produce infinite families of counterexamples to Jantzen's question posed in 1980 on the existence of Weyl -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 or.

AB - In this paper we produce infinite families of counterexamples to Jantzen's question posed in 1980 on the existence of Weyl -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 or.

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KW - tilting modules

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On Donkin's tilting module conjecture II: Counterexamples

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