Abstract

We construct a homomorphism $f$ from the braid group $B_{2n+2}$ on $2n+2$ strands to the Steinberg group $\mathrm{St}<!--FUNCTION\; APPLICATION-->(C_n,\mathbb{Z})$ associated with the Lie type $C_n$ and with integer coefficients. This homomorphism lifts the well-known symplectic representation (aka the integral Burau representation) of the braid group. We also describe the image and the kernel of $f$.

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