On isometric dilations of product systems of $C*$-correspondences and applications to families of contractions associated to higher-rank graphs Adam Skalski 47A2005C2046L0847A13multi-dimensional dilationsproduct systems of $C*$-correspondenceshigher-rank graphs Let $\mathbb{E}$ be a product system of $C^{*}$-correspondences over $\mathbb{N}_0^r$. Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of $\mathbb{E}$ are established and difference between regular and $^{*}$-regular dilations discussed. It is in particular shown that a minimal isometric dilation is $^{*}$-regular if and only if it is doubly commuting. The case of product systems associated with higher-rank graphs is analysed in detail. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3690 10.1512/iumj.2009.58.3690 en Indiana Univ. Math. J. 58 (2009) 2227 - 2252 state-of-the-art mathematics http://iumj.org/access/