$SL_n$ 内形的局部 Langlands 对应
表示论
2016-12-09 v3
摘要
设 F 为非阿基米德局部域。我们建立了群 所有内形的局部 Langlands 对应。该对应表现为一种双射：一方面是增强了 S-群不可约表示的 Langlands 参数的共轭类，另一方面是 所有内形的不可约容许表示空间的并集。我们在阿基米德情形下也证明了类似的结果。为解决 F 具有正特征的情形，我们采用了近域方法。我们证明了，当域相对于表示的深度足够接近时，该方法与 内形的局部 Langlands 对应是相容的。
引用
@article{arxiv.1305.2638,
title = {The local Langlands correspondence for inner forms of $SL_n$},
author = {Anne-Marie Aubert and Paul Baum and Roger Plymen and Maarten Solleveld},
journal= {arXiv preprint arXiv:1305.2638},
year = {2016}
}
备注
In the second version Theorem 5.3 was restricted to n' = n-1 and the proof was modified accordingly. Also references to the work of Ganapathy were added. It turned out that the proof of Theorem 4.4 in versions 1 and 2 was incorrect and beyond repair, so we removed this result in version 3. Consequently Theorems 4.4 and 6.1 (from v1 and v2) only remain valid with worse lower bounds