Publications

We define Lawrence-Krammer representation of the pure braid group $P_n$ on band generators. For $t=q^{-5/2}$ and $q^2\neq 1$, we prove that the complex specialization of Lawrence-Krammer representation $P_4\mapsto GL_6(\mathbb{Z}[q^{\pm 1}])$ is irreducible if and only if $q\neq e^{\pm \frac{2\pi i}{3}}$. A similar result for the pure braid group $P_3$ was done by Abdulrahim and Al-Tahan.