Extending irreducible braid representations to the 3-component loop braid group

In a recent paper [3] it is shown that irreducible representations of the three string braid group B-3 of dimension < 5 extend to representations of the three component loop braid group LB3. Further, an explicit 6-dimensional irreducible B-3-representation is given not allowing such an extension. In this note we give a necessary and sufficient condition, in all dimensions, on the components of irreducible representations of the modular group F such that sufficiently general representations extend to Gamma *c(3) S-3. As a consequence, the corresponding irreducible B-3 representations do extend to LB3.

Publication year:2016