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Title

REDUCIBILITY OF THE COHEN–WALES REPRESENTATION OF THE ARTIN GROUP OF TYPE Dn
Author

CLAIRE LEVAILLANT
Journal / Anthology

Journal of Knot Theory and Its Ramifications
Year: 2012
Volume: 21
Issue: 10
Description

We construct a linear representation of the CGW algebra of type Dn. This representation has degree n2 − n, the number of positive roots of a root system of type Dn. We show that the representation is generically irreducible, but that when the parameters of the algebra are related in a certain way, it becomes reducible. As a representation of the Artin group of type Dn, this representation is equivalent to the faithful linear representation of Cohen–Wales. We give a reducibility criterion for this representation as well as a conjecture on the semisimplicity of the CGW algebra of type Dn. Our proof is computer-assisted using Mathematica.
Subject

*Mathematics
Keywords

Cohen–Wales representation, Artin group.