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july 2020 Notes on functions of hyperbolic type
Nicolas Monod
Bull. Belg. Math. Soc. Simon Stevin 27(2): 167-202 (july 2020). DOI: 10.36045/bbms/1594346414

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 $\mathbf{SU}(1,n)$ and of its infinite-dimensional kin ${\rm Is}(\mathbf{H}_{\mathbf{C}}^{\infty})$. We further classify all the self-representations of ${\rm Is}(\mathbf{H}_{\mathbf{C}}^{\infty})$ that satisfy a compatibility condition for the subgroup ${\rm Is}(\mathbf{H}_{\mathbf{R}}^{\infty})$. 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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Nicolas Monod. "Notes on functions of hyperbolic type." Bull. Belg. Math. Soc. Simon Stevin 27 (2) 167 - 202, july 2020. https://doi.org/10.36045/bbms/1594346414

Information

Published: july 2020
First available in Project Euclid: 10 July 2020

zbMATH: 07242765
MathSciNet: MR4121370
Digital Object Identifier: 10.36045/bbms/1594346414

Subjects:
Primary: 43A35, 53A35, 53C50, 57S25

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 2 • july 2020
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