We consider varieties of representations and characters of
– and
–dimensional
orbifolds in semisimple Lie groups, and we focus on computing their dimension. For hyperbolic
–orbifolds,
we consider the component of the variety of characters that contains the holonomy
composed with the principal representation, and show that its dimension equals half
the dimension of the variety of characters of the boundary. We also show
that this is a lower bound for the dimension of generic components. We
furthermore provide tools for computing dimensions of varieties of characters of
–orbifolds,
including the Hitchin component. We apply this computation
to the dimension growth of varieties of characters of some
–dimensional
manifolds in
.
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