Mathematics & Computer Science Faculty Work
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
Recommended Citation
Jackson, Craig and Kerler, Thomas, "The Lawrence-Krammer-Bigelow Representations of the Braid Groups via Uq(s12)" (2011). Mathematics & Computer Science Faculty Work. 6.
https://digitalcommons.owu.edu/math_cs_pubs/6
Link Out URL
https://doi.org/10.1016/j.aim.2011.06.027