  We show how there is a natural action on the cohomology groups attached to
certain subgroups of GL_n(F) of the Hecke operators defined as elements in an
adelic double coset algebra.
  Our main result is, that if a system of eigenvalues for Hecke operators occur
in the cohomology groups with coefficients in certain modules, then by changing
the groups the system also occur in the cohomology groups with coefficients in
a 1-dimensional module.
