On Krammer's Representation of the Braid Group

Details On Krammer's Representation of the Braid Group On Krammer's Representation of the Braid Group

2000-02-16

arxiv.org/abs/math/0002136v1

Mathematics

Representation Theory

15 pages, 4 figures. Submitted to Math Research Letters

Scientific paper

A connection is made between the Krammer representation and the Birman-Murakami-Wenzl algebra. Inspired by a dimension argument, a basis is found for a certain irrep of the algebra, and relations which generate the matrices are found. Following a rescaling and change of parameters, the matrices are found to be identical to those of the Krammer representation. The two representations are thus the same, proving the irreducibility of one and the faithfulness of the other.

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