Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tangles of type $E_n$ and a reducibility criterion for the Cohen-Wales
  representation of the Artin group of type $E_6$   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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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom