ON A CERTAIN LOCAL IDENTITY FOR LAPID?MAO’S CONJECTURE AND FORMAL DEGREE CONJECTURE : EVEN UNITARY GROUP CASE
ON A CERTAIN LOCAL IDENTITY FOR LAPID?MAO’S CONJECTURE AND FORMAL DEGREE CONJECTURE : EVEN UNITARY GROUP CASE
复制标题
论拉皮德的某个局部恒等式？毛猜想和形式度猜想：偶数群情况
DOI：
10.1017/s1474748020000523
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发表时间：
2022
影响因子：
0.9
通讯作者：
Morimoto Kazuki
中科院分区：
文献类型：
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作者：
Morimoto Kazuki
Lapid和Mao提出了一个关于拟分裂约化群和亚群上自守形式的Whittaker-Fourier系数的显式公式的猜想，类似于Ichino-Ikeda猜想。他们还表明，这一猜想是减少到一定的地方单位的情况下，酉群。在这篇文章中，我们研究了偶酉群的情况。事实上，我们证明了这个本地身份的p-adic领域。此外，我们证明了这个地方的身份和一个精致的形式度猜想之间的等价性在任何地方领域的特征为零。由此，我们证明了p-adic域上的一个精化形式度猜想，并在一定的假设下得到了Whittaker-Fourier系数的一个显式表达式.
Lapid and Mao formulated a conjecture on an explicit formula of Whittaker–Fourier coefficients of automorphic forms on quasi-split reductive groups and metaplectic groups as an analogue of the Ichino–Ikeda conjecture. They also showed that this conjecture is reduced to a certain local identity in the case of unitary groups. In this article, we study the even unitary-group case. Indeed, we prove this local identity over p-adic fields. Further, we prove an equivalence between this local identity and a refined formal degree conjecture over any local field of characteristic zero. As a consequence, we prove a refined formal degree conjecture over p-adic fields and get an explicit formula of Whittaker–Fourier coefficients under certain assumptions.