  A new class of algebras have been introduced by Khovanov and Lauda and
independently by Rouquier. These algebras categorify one-half of the Quantum
group associated to arbitrary Cartan data. In this paper, we use the
combinatorics of Lyndon words to construct the irreducible representations of
those algebras associated to Cartan data of finite type. This completes the
classification of simple modules for the quiver Hecke algebra initiated by
Kleshchev and Ram.
