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

Abstract

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

34 pages, 17 figures

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