How to generate spinor representations in any dimension in terms of projection and nilpotent operators

We present a technique to construct a spinor space basis as products of certain nilpotents and projections formed from gamma(a) for which we only need to know that they obey the Clifford algebra. The technique works for all dimensions and signatures. We use this technique to deliver a concrete choice of gamma-matrices and Lorentz group generators for (fundamental representations of) spinors in a rather systematic and transparent way. We further develop the formalism by proposing the corresponding graphic presentation of basic states, which offers an easy way to see all the quantum numbers of states with respect to the generators of the Lorentz group, as well as transformation properties of the states under any element of the Clifford algebra. (C) 2002 American Institute of Physics.