  We study properties of irreducible and completely reducible representations
of finitely generated groups Gamma into reductive algebraic groups G in in the
context of the geometric invariant theory of the G-action on Hom(Gamma,G) by
conjugation.
  In particular, we study properties of character varieties,
X_G(Gamma)=Hom(Gamma,G)//G. We describe the tangent spaces to X_G(Gamma) in
terms of first cohomology groups of Gamma with twisted coefficients,
generalizing the well known formula.
  Let M be an orientable 3-manifold with a connected boundary F of genus > 1
and let X_G^g(F) be the subset of the G -character variety of F composed of
conjugacy classes of good representations. By a theorem of Goldman, X_G^g(F) is
a holomorphic symplectic manifold. We prove that the set of good
G-representations of pi_1(F) which extend to representations of pi_1(M) is an
isotropic submanifold of X_G^g(F). If these representations correspond to
reduced points of the G-character variety of M then this submanifold is
Lagrangian.
