  We determine the unipotent orbits attached to degenerate Eisenstein series on
general linear groups. This confirms a conjecture of David Ginzburg. This also
shows that any unipotent orbit of general linear groups does occur as the
unipotent orbit attached to a specific automorphic representation. The key
ingredient is a root-theoretic result. To prove it, we introduce the notion of
the descending decomposition, which expresses every Weyl group element as a
product of simple reflections in a certain way. It is suitable for induction
and allows us to translate the question into a combinatorial statement.
