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arXiv · 2506.17070

A diagrammatic approach to reflection functors

Haruto Murata
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Abstract

We construct reflection functors for quiver Hecke algebras associated with arbitrary symmetrizable Kac-Moody algebras, from a higher representation-theoretic viewpoint. These functors provide a categorification of Lusztig's braid group action on the quantum group. Similar functors were recently constructed independently by Kashiwara-Kim-Oh-Park via a different approach. Moreover, we prove that our reflection functors satisfy the braid relations as natural isomorphisms.

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Haruto Murata. 2025-06-20. A diagrammatic approach to reflection functors. https://arxiv.org/abs/2506.17070

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