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arXiv · 1606.08872

Fourier Coefficients for Degenerate Eisenstein Series and the Descending Decomposition

Yuanqing Cai
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Abstract

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.

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BibTeXRIS

Yuanqing Cai. 2016-06-28. Fourier Coefficients for Degenerate Eisenstein Series and the Descending Decomposition. https://doi.org/10.1007/s00229-017-0984-x

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