Local coordinates for SL(n,C) character varieties of finite volume   hyperbolic 3-manifolds
  Given a finite volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL(2,C) with the n-dimensional irreducible representation of SL(2,C) in SL(n,C). In this paper we give local coordinates of the SL(n,C)-character variety around this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps. 
Pere Menal-Ferrer, Joan Porti
math.GT