%0 Journal Article
%T The Lawrence-Krammer-Bigelow Representations of the Braid Groups via Quantum SL_2
%A Craig Jackson
%A Thomas Kerler
%J Mathematics
%D 2009
%I arXiv
%X We construct representations of the braid groups B_n on n strands on free Z[q,q^-1,s,s^-1]-modules W_{n,l} using generic Verma modules for an integral version of quantum sl_2. We prove that the W_{n,2} are isomorphic to the faithful Lawrence Krammer Bigelow representations of B_n after appropriate identification of parameters of Laurent polynomial rings by constructing explicit integral bases and isomorphism. We also prove that the B_n-representations W_{n,l} are irreducible over the fractional field Q (q,s).
%U http://arxiv.org/abs/0912.2114v2