It is known that the Lie superalgebra psl(2|2) with three central
extensions plays very important roles in the AdS/CFT correspondence
and the one-dimensional Hubbard model.
In this talk, I discuss the finite dimensional irreducible
representations of this algebra
and gives the complete list of them.
In particular, I will explain that there exist multiplets which is shorter than
so called "long multiplets" and longer than "short multiplet."
This is based the collaboration work with Alexander Movel (U. of Sydney),
arXiv:1405.3420.
