Complex hyperbolic representations of $$\textrm{PSL}_2(\textbf{R})$$

Abstract

We construct a two-parameter family of irreducible representations of $$\textrm{PSL}_2(\textbf{R})$$ 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.