  We study certain cases of convoluted Fourier coefficients of
$GL_n$-automorphic functions. We establish identities that express them in
terms of Fourier coefficients related to unipotent orbits. The most general
case that is studied is $(n)\circ(k,2^{n-1})$. The conclusions for this case is
only up to a conjecture that I state. However there are certain special cases
and other examples that are not based on any conjecture.
