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Lieven LeBruyn. Rationality and dense families of B(3) representations. arXiv/math.RA, 1003.1610, 2010.
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.
@article{LeBruyn2010a,
author={LeBruyn, Lieven},
title={Rationality and dense families of B(3) representations},
year={2010},
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.},
bib2html_pubtype ={Papers},
bib2html_rescat ={Representation Theory},
journal={arXiv/math.RA},
volume={1003.1610},
language={English},
bib2html_dl_html={http://arxiv.org/abs/1003.1610}
}
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