Suppose a finite group acts on a scheme X and a finite-dimensional Lie
algebra g. The corresponding equivariant map algebra is the Lie algebra M of
equivariant regular maps from X to g. We classify the irreducible
finite-dimensional representations of these algebras. In particular, we show
that all such representations are tensor products of evaluation representations
and one-dimensional representations, and we establish conditions ensuring that
they are all evaluation representations. For example, this is always the case
if M is perfect.