Another Proof of the Faithfulness of the Lawrence-Krammer Representation of the Braid Group B3. (25th June 2012) - Abdulrahim, Mohammad N.; Hariri, Mariam
Abstract : The Lawrence-Krammer representation of the braid group B n was proved to be faithful for n ≥ 3 by Bigelow and Krammer. In our paper, we give a new proof in the case n = 3 by using matrix computations. First, we prove that the representation of the braid group B 3 is unitary relative to a positive definite Hermitian form. Then we show the faithfulness of the representation by specializing the indeterminates q and t to complex numbers on the unit circle rather than specializing them to real numbers as what was done by Krammer.