For each 0<c<1, the operator system generated by four concrete operators on L2(S3)⊕C is not hyperrigid, while every irreducible representation of its C*-algebra restricts to a boundary representation.
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A Finite Dimensional Counterexample for Arveson's Hyperrigidity Conjecture
For each 0<c<1, the operator system generated by four concrete operators on L2(S3)⊕C is not hyperrigid, while every irreducible representation of its C*-algebra restricts to a boundary representation.