Mathematics – Group Theory
Scientific paper
2011-03-29
Mathematics
Group Theory
55 pages, 22 figures
Scientific paper
Using knot theory, we construct a linear representation of the CGW algebra of type $D_n$. This representation has degree $n^2-n$, the number of positive roots of a root system of type $D_n$. 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 $D_n$, 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 $D_n$. Our proof is computer-assisted using Mathematica.
No associations
LandOfFree
Reducibility of the Cohen-Wales representation of the Artin group of type $D_n$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Reducibility of the Cohen-Wales representation of the Artin group of type $D_n$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reducibility of the Cohen-Wales representation of the Artin group of type $D_n$ will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-163568