LAUSR

Abstract Let Γ be a group acting on a scheme X and on a Lie superalgebra g , both defined over an algebraically closed field of characteristic zero k . The corresponding equivariant map superalgebra M ( g , X ) Γ is the Lie superalgebra of Γ-equivariant regular maps from X to g . In this paper we complete the classification of finite-dimensional irreducible M ( g , X ) Γ -modules when g is a finite-dimensional simple Lie superalgebra, X is of finite type and Γ is a finite abelian group acting freely on the rational points of X , by classifying these M ( g , X ) Γ -modules in the case where g is a periplectic Lie superalgebra. We also describe extensions between irreducible modules in terms of homomorphisms and extensions between modules for certain finite-dimensional Lie superalgebras. As an application, one obtains the block decomposition of the category of finite-dimensional M ( g , X ) Γ -modules in terms of blocks and spectral characters of finite-dimensional Lie superalgebras.