Generators, relations and symmetries in pairs of 3x3 unimodular matrices

Denote the free group on two letters by F-2 and the SL(3, C) -representation variety of F-2 by R = Hom(F-2, SL(3, C). There is a SL(3, Q-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 C-9 mapping onto C-8. Our choice of generators exhibit Out(F-2) symmetries which allow for a succinct expression of the defining relations. (c) 2007 Elsevier Inc. All rights reserved.