Random walks and the symplectic representation of the braid group

Marc Soret, Marina Ville

We consider the symplectic representation $\ddot{I}{}_n$ of a braid group $B(n)$ in $Sp(2l,\mathbb{Z})$, for $l=\left[\frac{n-1}{2}\right]$. If $P$ is a polynomial on the $4l^2$ coefficients…