p-adic Galois对称对的纠缠周期与判别
Intertwining periods and distinction for p-adic Galois symmetric pairs
摘要：
我们认为区别的上下文中的$p$ -adic伽罗瓦对称空间的表示。利用诱导数据上的相似条件，给出了区分抛物线诱导表示的新的充分条件，并推导出区分抛物线诱导表示与尖点表示的一个特征.我们对典型群的结果作了进一步的解释，并给出了几个应用，特别是关于通过朗兰兹函性保持区别的应用。我们将我们的结果与Dipendra Prasad的猜想。
英文摘要：
We consider distinction of representations in the context of $p$-adic Galois symmetric spaces. We provide new sufficient conditions for distinction of parabolically induced representations in terms of similar conditions on the inducing data and deduce a characterization for distinction of representations parabolically induced from cuspidal. We explicate the results further for classical groups and give several applications, in particular, concerning the preservation of distinction via Langlands functoriality. We relate our results with a conjecture of Dipendra Prasad.
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