Generators, Relations and Symmetries in Pairs of 3x3 Unimodular Matrices
Algebraic Geometry
2008-04-30 v4 Commutative Algebra
Abstract
Denote the free group on two letters by F2 and the SL(3,C)-representation variety of F2 by R = Hom(F2, SL(3,C)). There is a SL(3,C)-action on the coordinate ring of R, and the geometric points of the subring of invariants is an affine variety X. We determine explicit minimal generators and defining relations for the subring of invariants and show X is a degree 6 hyper-surface in C9 mapping onto C8. Our choice of generators exhibit Out(F2) symmetries which allow for a succinct expression of the defining relations.
Keywords
Cite
@article{arxiv.math/0601132,
title = {Generators, Relations and Symmetries in Pairs of 3x3 Unimodular Matrices},
author = {Sean Lawton},
journal= {arXiv preprint arXiv:math/0601132},
year = {2008}
}
Comments
21 pages. This fourth version is the author's final version which includes new comments and some corrections