Finite Dimensional Representations of Khovanov-Lauda-Rouquier algebras   I: Finite Type
  We classify simple representations of Khovanov-Lauda-Rouquier algebras in finite type. The classification is in terms of a standard family of representations that is shown to yield the dual PBW basis in the Grothendieck group. Finally, we prove a conjecture describing the global dimension of these algebras. 
Peter J. McNamara
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