ON $\text{Sp}$ -DISTINGUISHED REPRESENTATIONS OF THE QUASI-SPLIT UNITARY GROUPS
ON $\text{Sp}$ -DISTINGUISHED REPRESENTATIONS OF THE QUASI-SPLIT UNITARY GROUPS
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ON $ ext{Sp}$ - 准分裂酉群的杰出表示
DOI：
10.1017/s1474748019000161
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发表时间：
2018
影响因子：
0.9
通讯作者：
Omer Offen
中科院分区：
文献类型：
--
作者：
Arnab Mitra;Omer Offen
本文研究了拟分裂酉群U_{2n}（E/F）关于p-adic域的二次扩张E/F的2n元表示的Sp_{2n}（F）-区别. Dijols和Prasad的一个猜想预言，没有调和表示是区别的。我们验证了这一点的一个大家庭的表示在MÜglin-Tadić分类的离散系列。我们进一步研究了一些家庭的非调和表示的区别。特别地，我们展示了$L$ -包没有区别的成员，转移到$\text{GL}_{2n}（E）$的$\text {Sp}_{2n}（E）$ -区别表示的基础变化。
Abstract We study $\text{Sp}_{2n}(F)$ -distinction for representations of the quasi-split unitary group $U_{2n}(E/F)$ in $2n$ variables with respect to a quadratic extension $E/F$ of $p$ -adic fields. A conjecture of Dijols and Prasad predicts that no tempered representation is distinguished. We verify this for a large family of representations in terms of the Mœglin–Tadić classification of the discrete series. We further study distinction for some families of non-tempered representations. In particular, we exhibit $L$ -packets with no distinguished members that transfer under base change to $\text{Sp}_{2n}(E)$ -distinguished representations of $\text{GL}_{2n}(E)$ .