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

Fourier Coefficients for Degenerate Eisenstein Series and the Descending Decomposition