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arXiv · 2501.06209

Quantum groups of Borcherds-Cartan type and Khovanov-Lauda-Rouquier algebras

Seok-Jin Kang·Young Rock Kim·Bolun Tong
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Abstract

We categorify a class of quantum groups associated with quivers, possibly with loops, by constructing the corresponding Khovanov-Lauda-Rouquier algebras (KLR) algebras $R$. We prove that the indecomposable projective $R$-modules realize the canonical basis of the negative part $U^-$ of the quantum group. Moreover, for $\Lambda \in P^+$, the cyclotomic KLR algebra $R^\Lambda$ provide a categorification of the irreducible highest weight $U$-module $V(\Lambda)$.

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Seok-Jin Kang, Young Rock Kim, Bolun Tong. 2024-12-30. Quantum groups of Borcherds-Cartan type and Khovanov-Lauda-Rouquier algebras. https://arxiv.org/abs/2501.06209

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