Indecomposable Representations of Special Linear Lie Superalgebras

The main result of this paper is a classification of finite-dimensional representations of the Lie superalgebras sl(m, 1) of supertraceless endomorphisms of the vector superspace of dimension (m1). The classification extends to the so-called singly atypical blocks of the Lie superalgebras sl(m, n), but there exist wild representation type blocks as soon as bothmandnare ≥ 2.