Parameters for which the Lawrence-Krammer representation is reducible

Details Parameters for which the Lawrence-Krammer representation is reducible Parameters for which the Lawrence-Krammer representation is reducible

2009-01-24

arxiv.org/abs/0901.3856v1

Mathematics

Representation Theory

32 pages, 6 figures

Scientific paper

We show that the Lawrence-Krammer representation based on two parameters that was used by Bigelow and independently Krammer to show the linearity of the braid group is generically irreducible, but that when its parameters are specialized to some nonzero complex numbers, the representation is reducible. To do so, we construct a representation of the BMW algebra inside the Lawrence-Krammer space. As a representation of the braid group, this representation is equivalent to the Lawrence-Krammer representation, where the two parameters of the algebra are related to the parameters of the Lawrence-Krammer representation. We give all the complex values of the parameters for which the representation is reducible and describe the invariant subspaces in some cases. We show that for these values of the parameters and other values, the BMW algebra is not semisimple.

Affiliated with

Also associated with

No associations

Rating

Parameters for which the Lawrence-Krammer representation is reducible 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 Parameters for which the Lawrence-Krammer representation is reducible, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Parameters for which the Lawrence-Krammer representation is reducible will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-503948