Quiver Hecke algebras for Borcherds-Cartan datum II

2024/06/03 by Bolun Tong, Wan Wu, Tong, Bolun +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2406.01050

openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give the crystal structure of the Grothendieck group G₀(R) of irreducible modules over the quiver Hecke algebra R constructed in \citeTW2023. This leads to the categorification of the crystal B(∞) of the quantum Borcherds algebra U_q(\mathscr g) and its irreducible highest weight crystal B(λ) for arbitrary Borcherds-Cartan data. Additionally, we study the cyclotomic categorification of irreducible highest weight U_q(\mathscr g)-modules.

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