Non-linear representations of extended supersymmetry with central charges

A new class of non-linear representations of N extended supersymmetry is found. These nonlinear realizations extend the Volkov-Akulov nonlinear realizations to include central charges which can also be non-linearly realized. The general construction of the corresponding non-linear Lagrangians is presented. The coupling to N extended supergravity provides the simultaneous occurrence of the Higgs and super-Higgs effects. The corresponding formulae for spin-3/2 gravitions and spin-1 vector boson masses are derived. (orig.)