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(infinity)). We further classify all the self-representations of Is(H-C(infinity)) that satisfy a compatibility condition for the subgroup Is(H-R(infinity)). It turns out in particular that translation lengths and Cartan arguments determine each other for these representations.
In the real case, we revisit earlier results and propose some further constructions.
WOS:000549353400002
2020-07-01
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