$\operatorname{Sp}(2,\mathbb{R})$极大抛物子群中半直积的几何分类
Geometric classification of semidirect products in the maximal parabolic subgroup of $\operatorname{Sp}(2,\mathbb{R})$
摘要：
我们分类共轭$\operatorname{GL}(2,\mathbb{R})$（更准确地说，块对角辛矩阵）内的所有半直积的最大抛物线的$\operatorname{Sp}(2,\mathbb{R})$通过一个基本的几何参数。这种分类已经建立了没有几何，根据更严格的概念等价，即共轭任意辛矩阵。本方法在更高维度中可能有用，并提供了一些见解。
英文摘要：
We classify up to conjugation by $\operatorname{GL}(2,\mathbb{R})$ (more precisely, block diagonal symplectic matrices) all the semidirect products inside the maximal parabolic of $\operatorname{Sp}(2,\mathbb{R})$ by means of an essentially geometric argument. This classification has already been established without geometry, under a stricter notion of equivalence, namely conjugation by arbitrary symplectic matrices. The present approach might be useful in higher dimensions and provides some insight.
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