On KZ-systems which are irreducible under the action of the symmetric group

We give a classification of KZ-systems that are irreducible under the actio n of the symmetric group. The proofs can be found in our thesis [10]. The m ain result is that almost all of these KZ-systems correspond to a represent ation of the braid group that factorizes through the lwahori-Hecke algebra of type A. Among the exceptions is a new representation of the braid group, for which we give an explicit description. (C) 2001 Academie des sciences/ Editions scientifiques et medicales Elsevier SAS.