Tangles of type En and a reducibility criterion for the Cohen–Wales representation of the Artin group of type E6

In this paper, we introduce tangles of type [Formula: see text] and construct a representation of the Birman–Murakami–Wenzl algebra (BMW algebra) of type [Formula: see text]. As a representation of the Artin group of type [Formula: see text], this representation is equivalent to the faithful Cohen–Wales representation of type [Formula: see text] that was used to show the linearity of the Artin group of type [Formula: see text]. We find a reducibility criterion for this representation and complex values of the parameters for which the algebra is not semisimple.