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

الأصل · EN

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