We study quasi-isometric embeddings of symmetric spaces and non-uniform irreducible lattices in semi-simple higher rank Lie groups. We show that any quasi-isometric embedding between symmetric spaces of the same rank can be decomposed into a product of quasi-isometric embeddings into irreducible symmetric spaces. We thus extend earlier rigidity results about quasi-isometric embeddings to the setting of semi-simple Lie groups. We also present some examples when the rigidity does not hold, including first examples in which every flat is mapped into multiple flats.

中文翻译：

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对称空间和晶格的准等距嵌入：可简化的情况

我们研究了半简单高阶李群中对称空间和非均匀不可约晶格的准等距嵌入。我们表明，相同秩的对称空间之间的任何准等距嵌入都可以分解为准等距嵌入到不可约对称空间的乘积。因此，我们将早期关于准等距嵌入的刚性结果扩展到半简单李群的设置。我们还提供了一些刚性不成立的例子，包括第一个例子，其中每个单位都映射到多个单位。