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arXiv · 1102.4677

Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras

Seok-Jin Kang·Masaki Kashiwara
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Abstract

In this paper, we prove Khovanov-Lauda's cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let $U_q(g)$ be the quantum group associated with a symmetrizable Cartan datum and let $V(Λ)$ be the irreducible highest weight $U_q(g)$-module with a dominant integral highest weight $Λ$. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra $R^Λ$ gives a categorification of $V(Λ)$.

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Seok-Jin Kang, Masaki Kashiwara. 2012-02-05. Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras. https://doi.org/10.1007/s00222-012-0388-1

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