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We introduce tangles of type $E_n$ and construct a representation of theBirman-Murakami-Wenzl algebra (BMW algebra) of type $E_6$. As a representationof the Artin group of type $E_6$, this representation is equivalent to thefaithful Cohen-Wales representation of type $E_6$ that was used to show thelinearity of the Artin group of type $E_6$. We find a reducibility criterionfor this representation and complex values of the parameters for which thealgebra is not semisimple.

Tangles of type $E_n$ and a reducibility criterion for the Cohen-Wales representation of the Artin group of type $E_6$