mirabolic子群的线性周期与Shalika局部周期及其推论
表示论
2018-08-01 v6
摘要
利用GL(n,F)的mirabolic子群上的线性周期，其中F是非阿基米德局部域，我们给出了能够区分离散序列和一般表示的GL(n,F)的最大Levi子群的列表。我们还得到了当n=2m为偶数时GL(n,F)的一般表示的局部外平方L-函数的函数方程。然后讨论了GL(2m,F)表示的Shalika模型与局部模型之间的关系。最后给出了尖点表示ρ使得GL(2m,F)的广义Steinberg表示St_k(ρ)具有局部模型的充要条件。
引用
@article{arxiv.1210.4307,
title = {Linear and Shalika local periods for the mirabolic group, and some consequences},
author = {Nadir Matringe},
journal= {arXiv preprint arXiv:1210.4307},
year = {2018}
}
备注
We corrected a minor mistake in the proof of Theorem 3.2. We modified the proof of previous Proposition 4.1., which was to allusive, and needed in fact some corrections. The argument in the proof of Theorem 4.1. to conclude that the epsilon factor is a unit was not correct, now it is