A Finite Dimensional Counterexample for Arveson's Hyperrigidity Conjecture

TL;DR

This paper presents a finite-dimensional counterexample to Arveson's hyperrigidity conjecture, showing an operator system that is not hyperrigid despite all irreducible restrictions having the unique extension property.

Contribution

It provides the first finite-dimensional counterexample to Arveson's hyperrigidity conjecture, challenging previous assumptions about the conjecture's scope.

Findings

Constructed a 4-operator operator system that is not hyperrigid

Demonstrated all irreducible restrictions have the unique extension property

Counterexample refutes the conjecture in finite dimensions

Abstract

We construct an operator system generated by $4$ operators that is not hyperrigid, although all restrictions of irreducible representations have the unique extension property.