Hecke operators for the principal congruence subgroup of the group Sp(n,?)

Abstract

One computes the action of the Hecke operators on the generalized theta series “with respect to progressions” and one obtains the Euler decomposition of the theta transformations of the modular Siegel forms relative to the principal congruence subgroups of an integral symplectic group. The results are based on the technique of the decomposition of symplectic polynomials.