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Extraspecial 2-groups and images of braid group representations

Jennifer Franko·Eric C. Rowell·Zhenghan Wang
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Abstract

We investigate a family of (reducible) representations of Artin's braid groups corresponding to a specific solution to the Yang-Baxter equation. The images of the braid groups under these representations are finite groups, and we identify them precisely as extensions of extra-special 2-groups. The decompositions of the representations into their irreducible constituents are determined, which allows us to relate them to the well-known Jones representations of the braid groups factoring over Temperley-Lieb algebras and the corresponding link invariants.

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Jennifer Franko, Eric C. Rowell, Zhenghan Wang. 2005-04-05. Extraspecial 2-groups and images of braid group representations. https://arxiv.org/abs/math/0503435

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