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Finite-dimensional representations of Artin’s braid group. (English) Zbl 0847.20035

Abikoff, William (ed.) et al., The mathematical legacy of Wilhelm Magnus. Groups, geometry and special functions. Conference on the legacy of Wilhelm Magnus, May 1-3, 1992, Polytechnic Univ. Brooklyn, NY, USA. Providence, RI: American Mathematical Society. Contemp. Math. 169, 123-132 (1994).
This article surveys some current aspects of the linear representation theory of Artin’s braid groups. In the first part, the (reduced) Burau representations are reviewed, and the connection to the Jones representations, the method of \(R\)-matrices are explained. In the second part a recent theorem due to J. Moody/D. D. Long-M. Paton is presented stating that the Burau representation is not faithful if the number of braid-strings is greater than or equal to 6.
For the entire collection see [Zbl 0801.00023].

MSC:

20F36 Braid groups; Artin groups
20C15 Ordinary representations and characters
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