Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification

We classify the admissible types of constraint (hermitian, holomorphic, withreality conditions on the bosonic sectors, etc.) for generalizedsupersymmetries in the presence of complex spinors. We further point out whichconstrained generalized supersymmetries admit a dual formulation. For both realand complex spinors generalized supersymmetries are constructed and classifiedas dimensional reductions of supersymmetries from {\em oxidized} space-times(i.e. the maximal space-times associated to $n$-component Clifford irreps). Weapply these results to sistematically construct a class of models describingsuperparticles in presence of bosonic tensorial central charges, deriving theconsistency conditions for the existence of the action, as well as theconstrained equations of motion. Examples of these models (which, in theirtwistorial formulation, describe towers of higher-spin particles) were firstintroduced by Rudychev and Sezgin (for real spinors) and later by Bandos andLukierski (for complex spinors).Comment: 32 pages, LaTe