论文标题
常规超矛盾表示的区别和二次基础变化
Distinction and quadratic base change for regular supercuspidal representations
论文作者
论文摘要
在本文中，我们根据Hakim和Murnaghan开发的机械来研究Prasad对常规超矛盾表示的猜想，以研究杰出的表示形式，以及Kaletha对常规超级替代表示参数化的基本工作。对于常规的超矛盾表示形式，我们对Prasad公式中出现的数值数量的新解释进行了一些新的解释，并将证据减少为Tori。然后，普拉萨德猜想的证据还原为比较上述过程中自然出现的各种二次字符的比较。我们还对这些角色有一些新的观察结果，并详细研究了它们之间的关系。对于一些特定的示例，我们显示了这些字符的巧合，这为Prasad的猜想提供了新的本地证明，用于这些群体的常规超矛盾表示。当e/f不受影响并且g是一般的准分数还原组时，我们还证明了Prasad对G（e）的常规超矛盾表示的猜想。
In this article, we study Prasad's conjecture for regular supercuspidal representations based on the machinery developed by Hakim and Murnaghan to study distinguished representations, and the fundamental work of Kaletha on parameterization of regular supercuspidal representations. For regular supercuspidal representations, we give some new interpretations of the numerical quantities appearing in Prasad's formula, and reduce the proof to the case of tori. The proof of Prasad's conjecture then reduces to a comparison of various quadratic characters appearing naturally in the above process. We also have some new observations on these characters and study the relation between them in detail. For some particular examples, we show the coincidence of these characters, which gives a new purely local proof of Prasad's conjecture for regular supercuspidal representations of these groups. We also prove Prasad's conjecture for regular supercuspidal representations of G(E), when E/F is unramified and G is a general quasi-split reductive group.
