The number of simple modules for the Hecke algebras of type G(r,p,n): (with an appendix by Xiaoyi Cui)

We derive a parameterization of simple modules for the cyclotomic Hecke algebras of type G(r,p,n) with p>1 and n⩾3 over fields of any characteristic coprime to p. We give explicit formulas for the number of simple modules over these cyclotomic Hecke algebras.