Braid groups and symplectic Steinberg groups

Abstract

We construct a homomorphism f from the braid group B2n+2 on 2n + 2 strands to the Steinberg group St(Cn, Z) associated with the Lie type Cn and with integer coefficients. This homomorphism lifts the well-known symplectic representation of the braid groups. We also describe the image and the kernel of f .