Invariants of pairs in SL(4,C) and SU(3,1)
  We describe a minimal global coordinate system of order 30 on the SL(4,C)-character variety of a rank 2 free group. Using symmetry within this system, we obtain a smaller collection of 22 coordinates subject to 5 further real relations that determine conjugation classes of generic pairs of matrices in SU(3,1). 
Krishnendu Gongopadhyay, Sean Lawton
math.AG math.DG math.RT