  Varagnolo-Vasserot and Rouquier proved that, in a symmetric generalized
Cartan matrix case, the simple modules over the quiver Hecke algebra with a
special parameter correspond to the upper global basis. In this note we show
that the simple modules over the quiver Hecke algebras with a generic parameter
also correspond to the upper global basis in a symmetric generalized Cartan
matrix case.
