Extraspecial 2-groups and images of braid group representations
By Jennifer M. Franko, Eric C. Rowell, Zhenghan Wang. 2005
91 citations recorded by the source corpus.
We investigate a family of (reducible) representations of the braid groups Bn corresponding to a specific solution to the Yang‐Baxter equation. The images of Bn 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 Bn factoring over Temperley‐Lieb algebras and the corresponding link invariants.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5d11e270f85444db1eb6685ad228652fe4b666c0
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A Finiteness Property for Braided Fusion Categories (2009, background): “Various cases related to quantum groups at roots of unity, Hecke and BMW algebras, and finite group doubles have been studied in the literature, see [11, 13, 14, 20, 21, 24, 27].”
- Braid group representations from twisted quantum doubles of finite groups (2007, background): “This has been carried out to some extent for the braided tensor categories coming from quantum groups and polynomial link invariants at roots of unity [7, 8, 9, 10, 11, 12, 13].”