Cyclotomic Hecke Algebras of G(r, p, n)

In this note, we find a monomial basis of the cyclotomic Hecke algebra H-r,H-p,H-n of G(r,p,n) and show that the Ariki-Koike algebra H-r,(n) is a free module over H-r,H-p,H-n, using the Grobner-Shirshovbasistheory. For each irreducible representation of H-r,(p),(n), we give a polynomial basis consisting of linear combinations of the monomials corresponding to cozy tableaux of a given shape.