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

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