TITLE  :
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  Complex reflection groups, braid groups, Hecke algebras
  
AUTHORS :
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  Michel Brou\'e, Gunter Malle, Rapha\"el Rouquier

ADRESSES :
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Michel Brou\'e :
  Universit\'e Paris 7 Denis--Diderot
  et Institut Universitaire de France,
  Case 7012,
  2 Place Jussieu, F--75251 Paris Cedex 05, France

Gunter Malle:
  I.W.R., Im Neuenheimer Feld 368,
  D--69120 Heidelberg, Germany

Rapha\"el Rouquier~:
  UMR 9994 du CNRS,
  Universit\'e Paris 7 Denis--Diderot,
  Case 7012,
  2 Place Jussieu, F--75251 Paris Cedex 05, France


ABSTRACT :
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  Presentations ``\`a la Coxeter'' are given for all (irreducible) 
  finite complex reflection groups.
  They provide presentations for the corresponding generalized braid
  groups (for all but six cases),
  which allow us to generalize some of the known properties of finite
  Coxeter groups and their associated braid groups, such as the
  computation of the center of the braid group and the construction
  of deformations of the finite group algebra
  (Hecke algebras). We introduce monodromy representations of the
  braid groups which factorize through the Hecke algebras,
  extending results of Cherednik, Opdam, Kohno and others.


STATUS : 
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  Preprint.