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

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 $V(\Lambda )$ be the irreducible highest weight $U_q(g)$-module with a dominant integral highest weight $\Lambda$. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra $R^{\Lambda }$ gives a categorification of $V(\Lambda )$.

Typoes corrected

References in corpus (3)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras

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