Tangles of type En and a reducibility criterion for the Cohen-Wales representation of the Artin group of type E6
Abstract
We introduce tangles of type En and construct a representation of the Birman-Murakami-Wenzl algebra (BMW algebra) of type E6. As a representation of the Artin group of type E6, this representation is equivalent to the faithful Cohen-Wales representation of type E6 that was used to show the linearity of the Artin group of type E6. 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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