We construct a two-parameter family of irreducible representations of PSL₂(R) PSL 2 ( R ) in the isometry group of the infinite-dimensional complex hyperbolic space. To this end, we introduce the notion of horospherical combination of two representations. Our family then appears as horospherical combinations of two known one-parameter families.
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Gonzalo Emiliano Ruiz Stolowicz (2024) studied this question.