Volume 10, issue 4 (2010)

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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 $\alpha ,s$. For $\alpha ,s$ 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 $\alpha ,s$ are algebraically independent.

Keywords
braid group, representations, Zariski closure, unitarisability, Birman–Wenzl–Murakami algebra
Primary: 20F36
Secondary: 20C99