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arXiv · 2406.01050

Quiver Hecke algebras for Borcherds-Cartan datum II

Bolun Tong·Wan Wu
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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 $U_q(\mathscr g)$ and its irreducible highest weight crystal $B(\lambda)$ for arbitrary Borcherds-Cartan data. Additionally, we study the cyclotomic categorification of irreducible highest weight $U_q(\mathscr g)$-modules.

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BibTeXRIS

Bolun Tong, Wan Wu. 2024-06-03. Quiver Hecke algebras for Borcherds-Cartan datum II. https://arxiv.org/abs/2406.01050

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