Linearity of artin groups of finite type

Recent results on the linearity of braid groups are extended in two ways. We generalize the Lawrence Krammer representation as well as Krammer’s faithfulness proof for this linear representation to Artin groups of finite type. This paper was written during a stay of the first author at Caltech. He wants to thank the institute for its hospitality. Shortly after we circulated a preprint of the present paper, we learned that Digne had obtained similar results.