Braid Representations from Unitary Braided Vector Spaces

Abstract

We investigate braid group representations associated with unitary braided vector spaces, focusing on a conjecture that such representations should have virtually abelian images in general and finite image provided the braiding has finite order. We verify this conjecture for the two infinite families of Gaussian and group-type braided vector spaces, as well as the generalization to quasi-braided vector spaces of group-type.