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On Krammer's representation of the braid group

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Abstract.

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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Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY 10027, USA , , , , , , US

    Matthew G. Zinno

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  1. Matthew G. Zinno
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Received: 16 April 2000 / Published online: 23 July 2001

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Zinno, M. On Krammer's representation of the braid group. Math Ann 321, 197–211 (2001). https://doi.org/10.1007/PL00004501

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  • DOI: https://doi.org/10.1007/PL00004501

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