English

Rationality and dense families of B(3) representations

Rings and Algebras 2010-03-09 v1 Representation Theory

Abstract

Every irreducible component of the variety of semi-simple n-dimensional representations of the modular group has a Zariski dense subset contained in the image of an etale map from a rational quotient variety of representations of a fixed quiver Q. As an application we prove that there is a unique component of 6-dimensional representations of the three string braid group B(3) able to detect braid-reversion. Further, we give explicit rational parametrizations of dense families of simple B(3)-representations in all dimensions < 12.

Keywords

Cite

@article{arxiv.1003.1610,
  title  = {Rationality and dense families of B(3) representations},
  author = {Lieven Le Bruyn},
  journal= {arXiv preprint arXiv:1003.1610},
  year   = {2010}
}