What is the root system for the special unitary lie algebra $\mathfrak{su}(p, q)$. Remind that these are matrices of the form $\left( \begin{array}{cc} X & Y \\ \overline{Y}^t & Z \\ \end{array} \right) $, where $\overline{X}^t=-X$, $\overline{Z}^t=-Z$, and $tr(X)+tr(Z)=0$. Also is there any reference regarding the action of the Lie group $SU(p, q)$ on complex projective space? Thanks.