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Braids inside the Birman–Wenzl–Murakami algebra

Ivan Marin

Algebraic & Geometric Topology 10 (2010) 1865–1886
Abstract

We determine the Zariski closure of the representations of the braid groups that factor through the Birman–Wenzl–Murakami algebra, for generic values of the parameters α,s. For α,s of modulus 1 and close to 1, we prove that these representations are unitarizable, thus deducing the topological closure of the image when in addition α,s are algebraically independent.

Keywords
braid group, representations, Zariski closure, unitarisability, Birman–Wenzl–Murakami algebra
Mathematical Subject Classification 2000
Primary: 20F36
Secondary: 20C99
References
Publication
Received: 8 February 2010
Revised: 7 June 2010
Accepted: 21 June 2010
Published: 9 September 2010
Authors
Ivan Marin
Institut de Mathématiques de Jussieu
Université Paris 7
175 rue du Chevaleret
75013 Paris
France
http://www.people.math.jussieu.fr/~marin