Notes on functions of hyperbolic type

Functions of hyperbolic type encode representations on real or complex hyperbolic spaces, usually infinite-dimensional.

These notes set up the complex case. As applications, we prove the existence of a non-trivial deformation family of representations of SU(1,n) and of its infinite-dimensional kin Is(**H _{C}**). We further classify all the self-representations of Is(

In the real case, we revisit earlier results and propose some further constructions.

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[Publications][Nicolas Monod]