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

preprint2011arXivOpen access

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.

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

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