Title: High-dimensional representations of the 3-component loop braid group
Abstract: In a recent paper here arXiv:1508.0005 it is shown that irreducible representations of the three string braid group $B_3$ of dimensions $\leq 5$ extend to representations of the 3-component loop braid group $LB_3$. Further, an explicit $6$-dimensional irreducible $B_3$-representation is given that does not extend. In this note we give a necessary and sufficient condition, in all dimensions, on the components of irreducible representations of the modular group $\Gamma$ such that sufficiently general representations extend to $\Gamma \ast_{C_3} S_3$. As a consequence, the corresponding irreducible $B_3$-representations do extend to $LB_3$.
Publication Year: 2015
Publication Date: 2015-08-01
Language: en
Type: article
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot