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

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

2011-02-23

arxiv.org/abs/1102.4677v4

Mathematics

Quantum Algebra

Typoes corrected

Scientific paper

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 $V(\Lambda)$.

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