Maximality of correspondence representations

In this paper, we fully characterize maximal representations of a C*-correspondence, thereby strengthening several earlier results. We demonstrate the maximality criteria through diverse examples. We also describe the noncommutative Choquet boundary and provide additional counterexamples to Arveson's hyperrigidity conjecture following the counterexample recently found by the author and Dor-On. Furthermore, we identify several classes of correspondences for which the hyperrigidity conjecture holds.