局部对称空间的可变性：乘积情况

Pub Date : 2024-05-03 DOI:10.1007/s10711-024-00904-4

Tobias Weich, Lasse L. Wolf

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引用次数: 0

摘要

让\(X=X_1\times X_2\)是两个非紧密类型的一阶对称空间的乘积，并且\(\Gamma \)是\(G_1\times G_2\)中的一个无扭离散子群。我们证明\(\Gamma \backslash (X_1\times X_2)\)的谱与\(\Gamma \)在两个因子定义的两个方向上的渐近增长有关。我们得到，对于一大类 \(\Gamma \) 来说，\(L^2(\Gamma \backslash (G_1 \times G_2))\) 是有节制的。

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Temperedness of locally symmetric spaces: the product case

Let \(X=X_1\times X_2\) be a product of two rank one symmetric spaces of non-compact type and \(\Gamma \) a torsion-free discrete subgroup in \(G_1\times G_2\). We show that the spectrum of \(\Gamma \backslash (X_1\times X_2)\) is related to the asymptotic growth of \(\Gamma \) in the two directions defined by the two factors. We obtain that \(L^2(\Gamma \backslash (G_1 \times G_2))\) is tempered for a large class of \(\Gamma \).

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