关于复数 $p$-adic $\mathbf{GL}_n$ 表示的几何比较
表示论
2026-03-19 v3
摘要
本文采用几何方法研究 的可容许表示与 的未加扰表示之间的关系。我们证明，由第一作者构建的 与 的Langlands参数空间之间的几何关系，与Chan-Wong最近代数定义的函子兼容。随后我们证明，所述关系将 上的翻译函子与 上的部分Bernstein-Zelevinskii导数函子相互作用，为Chan-Wong的某些结果提供了纯粹的几何对应物。本工作的技术将在后续研究中扩展至实数和 -adic经典群，用于研究其Arthur包。
引用
@article{arxiv.2504.15653,
title = {On a geometric comparison of representations of complex and $p$-adic $\mathbf{GL}_n$},
author = {Taiwang Deng and Chang Huang and Bin Xu and Qixian Zhao},
journal= {arXiv preprint arXiv:2504.15653},
year = {2026}
}
备注
47 pages. v3: relations between translations, derivatives, and their geometric counterparts were made precise; several expositional improvements were made; some typos, signs and conventional issues were fixed. v2: changed the title into a more accurate one; added a summary of main results to the introduction; rewritten the proof of 3.3.9 into a more readable one; corrected several typos