Algebra and Geometry Seminar

Series: Algebra & Geometry Seminar Series

Tangles of types En and a representation of the Birman-Murakami-Wenzl algebra of type E6

Claire Levailllant, Department of Mathematics, USC,

We show that as a representation of the Artin group, this representation is equivalent to the parameters based representation which was introduced by Cohen and Wales as a generalization of the Lawrence-Krammer representation of the braid group. The latter representation became famous as it is the only known representation of the braid group that is faithful. Likewise, the Cohen-Wales representation of the Artin group of type E6 is the only known faithful representation of the Artin group of type E6.

We use our representation to find a reducibility criterion for the faithful Cohen-Wales representation, depending on the values of its two parameters. We further derive values of the parameters for which the Birman-Murakami-Wenzl algebra of type E6 is not semisimple.

This work was achieved after the completion of my Ph.D. at Caltech under David Wales (1939-2023). This talk is given to honor his memory.

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