Fourier Coefficients for Degenerate Eisenstein Series and the Descending Decomposition
Representation Theory
2020-04-28 v1 Combinatorics
Number Theory
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.
Keywords
Cite
@article{arxiv.1606.08872,
title = {Fourier Coefficients for Degenerate Eisenstein Series and the Descending Decomposition},
author = {Yuanqing Cai},
journal= {arXiv preprint arXiv:1606.08872},
year = {2020}
}