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.