Automorphic functionals for the minimal representations of groups of type Dₙ and Eₙ

The minimal representation Π of G( A) for a split simply-connected group G of type D or E admits a realization on a space of functions S(X( A)) for a variety X. In this paper we write explicitly an automorphic, i.e. $G(F)$-invariant, functional on S(X( A)).