Resolutions of standard modules over KLR algebras of type A

Buursma, Doeke; Kleščev, Aleksandr S.‏ ‎; Steinberg, David J.

doi:10.1112/jlms.12400

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Resolutions of standard modules over KLR algebras of type A

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Kleščev, Aleksandr S.‏ ‎
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/jlms.12400
(Publisher version)

https://doi.org/10.48550/arXiv.1906.11376
(Preprint)

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Citation

Buursma, D., Kleščev, A. S. ‎., & Steinberg, D. J. (2021). Resolutions of standard modules over KLR algebras of type A. Journal of the London Mathematical Society, 103(3), 1035-1065. doi:10.1112/jlms.12400.

Cite as: https://hdl.handle.net/21.11116/0000-0008-AEFE-7

Abstract

Khovanov-Lauda-Rouquier algebras $R_\theta$ of finite Lie type are affine quasihereditary with standard modules $\Delta(\pi)$ labeled by Kostant partitions $\pi$ of $\theta$. In type $A$, we construct explicit projective
resolutions of standard modules $\Delta(\pi)$.