In this work we use the q-oscillator formalism to construct the atypical
(short) supersymmetric representations of the centrally extended Uq (su(2|2))
algebra. We then determine the S-matrix describing the scattering of arbitrary
bound states. The crucial ingredient in this derivation is the affine extension
of the aforementioned algebra.Comment: 44 pages, 3 figures. v2: minor correction
