G T ] 4 A pr 2 00 2 The Lawrence-Krammer representation

  title={G T ] 4 A pr 2 00 2 The Lawrence-Krammer representation},
  author={Stephen J. Bigelow},
The Lawrence-Krammer representation of the braid groups recently came to prominence when it was shown to be faithful by myself and Krammer. It is an action of the braid group on a certain homology module H2(C̃) over the ring of Laurent polynomials in q and t . In this paper we describe some surfaces in C̃ representing elements of homology. We use these to give a new proof that H2(C̃) is a free module. We also show that the (n− 2, 2) representation of the Temperley-Lieb algebra is the image of a… CONTINUE READING

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