COMPLEX REFLECTION GROUPS, BRAID-GROUPS, HECKE ALGEBRAS

Presentations ''a la Coxeter'' are given for all (irreducible) finite complex reflection groups. They provide presentations for the correspo nding generalized braid groups (for all but six cases), which allow us to generalize some of the known properties of finite Coxeter groups a nd their associated braid groups, such as the computation of the cente r of the braid group and the construction of deformations of the finit e group algebra (Hecke algebras). We introduce monodromy representatio ns of the braid groups which factorize through the Hecke algebras, ext ending results of Cherednik, Opdam, Kohno and others.