We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative \(\mathrm{SU}(2,1)\)-character varieties of the quadruply punctured sphere are described and applied to the study of length 5 relations.

中文翻译：

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特殊的椭圆异构体，相对$$ \ mathrm {SU}（2,1）$$ SU（2，1）-字符种类和弯曲

我们研究复双曲平面中特殊椭圆形的等距之间的关系。长度2、3和4的关系已完全分类。描述了四重打孔球体的一些相对\（\ mathrm {SU}（2,1）\）-个字符变体，并将其应用于长度5关系的研究。