Suppose a group Γ acts on a scheme X and a Lie superalgebra
g. The corresponding equivariant map superalgebra is the Lie
superalgebra of equivariant regular maps from X to g. We
classify the irreducible finite dimensional modules for these superalgebras
under the assumptions that the coordinate ring of X is finitely generated,
Γ is finite abelian and acts freely on the rational points of X, and
g is a basic classical Lie superalgebra (or sl(n,n),
n>0, if Γ is trivial). We show that they are all (tensor products
of) generalized evaluation modules and are parameterized by a certain set of
equivariant finitely supported maps defined on X. Furthermore, in the case
that the even part of g is semisimple, we show that all such
modules are in fact (tensor products of) evaluation modules. On the other hand,
if the even part of g is not semisimple (more generally, if
g is of type I), we introduce a natural generalization of Kac
modules and show that all irreducible finite dimensional modules are quotients
of these. As a special case, our results give the first classification of the
irreducible finite dimensional modules for twisted loop superalgebras.Comment: 27 pages. v2: Section numbering changed to match published version.
Other minor corrections. v3: Minor corrections (see change log at end of
introduction