Generalized graded Hecke algebra for complex reflection group of type   G(r,1,n)
  We study the representation theory of a generalized graded Hecke algebra associated to a complex reflection group of type G(r,1,n), defined by Ram and Shepler. We use a realization of this algebra in the corresponding symplectic reflection algebra to prove a PBW theorem. We define principal series modules and prove an irreducibility criterion for them. 
C. Dezelee