Title

The Lawrence-Krammer-Bigelow Representations of the Braid Groups via Uq(s12)

Document Type

Article

Publication Date

2011

Publication Title

Advances in Mathematics

Volume Number

228

Issue Number

3

DOI

10.1016/j.aim.2011.06.027

Abstract

We construct representations of the braid groups Bn on n strands on free Z[q±1, s±1] -modules Wn,l using generic Verma modules for an integral version of Uq(sl2). We prove that the Wn,2 are isomorphic to the faithful Lawrence–Krammer–Bigelow representations of Bn after appropriate identification of parameters of Laurent polynomial rings by constructing explicit integral bases and isomorphism. We also prove that the Bn-representations are irreducible over the fractional field Q(q,s).

ISSN

0001-8708

First Page

1689

Last Page

1717

Link Out URL

https://doi.org/10.1016/j.aim.2011.06.027

Share

COinS