Quiver Hecke algebras for Borcherds-Cartan datum II

Bolun Tong; Wan Wu

paper

Quiver Hecke algebras for Borcherds-Cartan datum II

arXiv:2406.01050

Abstract

We give the crystal structure of the Grothendieck group $G_{0} (R)$ of irreducible modules over the quiver Hecke algebra $R$ constructed in \cite{TW2023}. This leads to the categorification of the crystal $B (\infty)$ of the quantum Borcherds algebra $U_{q} (g)$ and its irreducible highest weight crystal $B (λ)$ for arbitrary Borcherds-Cartan data. Additionally, we study the cyclotomic categorification of irreducible highest weight $U_{q} (g)$ -modules.