Singular Rouquier complexes

Patimo, Leonardo

doi:10.1112/plms.12483

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Journal Article

Singular Rouquier complexes

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Patimo, Leonardo
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/plms.12483
(Publisher version)

https://doi.org/10.48550/arXiv.1908.10966
(Preprint)

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Patimo-Singular Rouquier complexes_2022.pdf
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Citation

Patimo, L. (2022). Singular Rouquier complexes. Proceedings of the London Mathematical Society, 125(6), 1332-1352. doi:10.1112/plms.12483.

Cite as: https://hdl.handle.net/21.11116/0000-000B-464B-3

Abstract

We generalize the construction of Rouquier complexes to the setting of one-sided singular Soergel bimodules. Singular Rouquier complexes are defined by taking
minimal complexes of restricted Rouquier complexes. We show that they retain many of the properties of ordinary Rouquier complexes: they are Δ-split, they satisfy a vanishing formula, and when Soergel’s conjecture holds
they are perverse. As an application, we establish Hodge theory for singular Soergel bimodules.