Abstract
The Lawrence-Krammer representation of the braid group was proved to be faithful for by Bigelow and Krammer. In our paper, we give a new proof in the case by using matrix computations. First, we prove that the representation of the braid group 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.
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