On Krammer's representation of the braid group
By Matthew G. Zinno. 2000
54 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7e1249eeca9779fb2b9fe2e97411e4de3a19f42d
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In Geometry and Topology
- J. Birman
- Tara E. Brendle
- Daan Krammer
- Juan González-Meneses
- Stephen Bigelow
- Luis Paris
- Benson Farb
- Dany Margalit
In Mathematical Physics
- J. Birman
- Tara E. Brendle
- Daan Krammer
- Juan González-Meneses
- Stephen Bigelow
- Luis Paris
- Benson Farb
- Dany Margalit
Citations in the corpus
- Braid groups are linear (2004, background): “Zinno [19] recently showed the representation to be a summand of the Birman-Wenzl algebra [6].”
- Braids: A Survey (2004, methodology): “Theorem 15 [137] The Lawrence-Krammer representation of Bn is equivalent to the (n− 2) × 1 irreducible representation of the BMW algebra.”