  We develop explicit formulas for Hecke operators of higher genus in terms of
spherical coordinates. Applications are given to summation of various
generating series with coefficients in local Hecke algebra and in a tensor
product of such algebras. In particular, we formulate and prove Rankin's lemma
in genus two. An application to a lifting from (GSp2 \times GSp2) to GSp4 is
given using Ikeda-Miyawaki constructions.
