Capelli’s Method of Variabili Ausiliarie, Superalgebras and Geometric Calculus

Capelli’s technique of variabili ausiliarie [8] — or “virtual variables”, as we prefer to call them — has been proved to be a useful tool in order to unify concepts and simplify computations in a variety of problems of invariant theory and its applications. In our opinion, Capelli’s technique finds its natural setting and acquires a much greater effectiveness in the context of supersymmetric algebras and Lie superalgebra actions; specifically, the technique of virtual variables acquires a special suppleness when the virtual variables are allowed to have a different signature than the signature of the variables one starts with.