2025/06/20 by Murata, Haruto
Mathematics · #16T20 #18N25 #20C08 #20G42 #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2506.17070
openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.