# Riesz operators and $L^{p}$-boundary representations for hyperbolic groups

## TL;DR

This paper explores the relationship between Riesz operators and Lp-boundary representations of hyperbolic groups, establishing conditions for irreducibility based on the injectivity of these operators.

## Contribution

It provides a new criterion linking Riesz operator injectivity to the irreducibility of boundary representations in hyperbolic groups.

## Key findings

- Lp-boundary representations are irreducible iff Riesz operators are injective.
- Established a characterization of irreducibility for hyperbolic group representations.
- Connected operator theory with geometric group properties.

## Abstract

We investigate Lp-boundary representations of hyperbolic groups. We prove that such representations are irreducible if and only if the corresponding Riesz operators are injective.