Notes on functions of hyperbolic type

2018/07/11 by Monod, Nicolas · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Metric Geometry (math.MG) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1807.04157

Abstract

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 Isom(H^∞_C). We further classify all the self-representations of Isom(H^∞_C) that satisfy a compatibility condition for the subgroup Isom(H^∞_R). 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.

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