Published online by Cambridge University Press: 20 November 2018
An equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) $X$ to a queer Lie superalgebra
$\mathfrak{q}$ that are equivariant with respect to the action of a finite group
$\Gamma $ acting on
$X$ and
$\mathfrak{q}$ . In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that
$\Gamma $ is abelian and acts freely on
$X$ . We show that such representations are parameterized by a certain set of
$\Gamma $ -equivariant finitely supported maps from
$X$ to the set of isomorphism classes of irreducible finite-dimensional representations of
$\mathfrak{q}$ . In the special case where
$X$ is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.