Some spaces of representations of orbifold fundamental groups, and their dimensions

Our starting point is a canonical representation of
an orbifold fundamental group into a Lie group.  Typically this representation
is not deformable, owing (for example) to Mostow rigidity.  Since our aim is
to deform, we circumvent this rigidity by representing further into a
larger target group.  Having thus obtained a deformation space of
representations, we see how its dimension can be determined.  The target groups
we shall consider are SL(n,R) for n at least 3 and the
exceptional Lie group G_2.