论文标题
在古典群体的本地亚瑟数据包上的封闭顺序猜想
The closure ordering conjecture on local Arthur packets of classical groups
论文作者
论文摘要
在本文中，我们证明了$ \ mathrm {g} _n = \ mathrm {sp} _ {2n}，\ mathrm {so} _ {so} _ {2n+1} $ opperistion的本地$ l $ l $ -l $ - 代表的代表体上的封闭订购。确切地说，在本地Arthur数据包中的任何表示$π$中，vogan品种中$π$的本地$ l $ - 参数的关闭必须包含对应于$ $ψ$的本地$ l $ - 参数。这个猜想揭示了当地的亚瑟小包的几何特性，并受到亚当斯，巴巴斯和沃根的作品的启发，以及在ABV宠物上的坎宁安，菲奥里，穆萨伊，穆斯豪，穆萨伊和Xu的作品。作为一种应用，对于一般的准切片连接的还原组，我们表明封闭订购的猜想意味着在某些合理的假设下，Shahidi猜想增强了。这为增强的Shahidi猜想提供了一个框架。我们为$ \ mathrm {g} _n $验证这些假设，因此给出了增强的Shahidi猜想的新证明。最后，我们表明其他亚瑟数据包不能完全包含在其他包装中，这与阿奇米德本地领域的情况形成鲜明对比，并且有其自身的兴趣。
In this paper, we prove the closure ordering conjecture on the local $L$-parameters of representations in local Arthur packets of $\mathrm{G}_n=\mathrm{Sp}_{2n}, \mathrm{SO}_{2n+1}$ over a non-Archimedean local field of characteristic zero. Precisely, given any representation $π$ in a local Arthur packet $Π_ψ$, the closure of the local $L$-parameter of $π$ in the Vogan variety must contain the local $L$-parameter corresponding to $ψ$. This conjecture reveals a geometric nature of local Arthur packets and is inspired by the work of Adams, Barbasch, and Vogan, and the work of Cunningham, Fiori, Moussaoui, Mracek, and Xu, on ABV-packets. As an application, for general quasi-split connected reductive groups, we show that the closure ordering conjecture implies the enhanced Shahidi conjecture, under certain reasonable assumptions. This provides a framework towards the enhanced Shahidi conjecture in general. We verify these assumptions for $\mathrm{G}_n$, hence give a new proof of the enhanced Shahidi conjecture. At last, we show that local Arthur packets cannot be fully contained in other ones, which is in contrast to the situation over Archimedean local fields and has its own interests.
