Integral basis theorem of cyclotomic Khovanov-Lauda-Rouquier algebras of type A

In this paper we prove that the cyclotomic Khovanov-Lauda-Rouquier algebras in type A, RnΛ, are Z-free. We then extend the graded cellular basis of RnΛ constructed by Hu and Mathas to Rn and use this basis to give a classification of all irreducible Rn-modules.