  The aim of this work is to study finite dimensional representations of the
Lie superalgebra psl(2|2) and their tensor products. In particular, we shall
decompose all tensor products involving typical (long) and atypical (short)
representations as well as their so-called projective covers. While tensor
products of long multiplets and projective covers close among themselves, we
shall find an infinite family of new indecomposables in the tensor products of
two short multiplets. Our note concludes with a few remarks on possible
applications to the construction of AdS_3 backgrounds in string theory.
