High-dimensional representations of the 3-component loop braid group
Faculty of Sciences. Mathematics and Computer Science
, p. 1-5
University of Antwerp
In a recent paper here arXiv:1508.0005 it is shown that irreducible representations of the three string braid group B3 of dimensions ≤5 extend to representations of the 3-component loop braid group LB3. Further, an explicit 6-dimensional irreducible B3-representation is given that does not extend. In this note we give a necessary and sufficient condition on the components of irreducible B3-representations, in arbitrary dimensions, such that sufficiently general representations in that component do extend to LB3.