I am looking for a reference where the relative root system, the relative system of simple roots, and parabolic $\Bbb R$-subgroups for the real algebraic group ${\rm SU}(p,q)$ are explicitly computed.

More generally, let $F$ be a field of characteristic 0, $L/F$ a quadratic extension, and $H$ be an $L/F$-Hermitian form on $L^n$. Write $G={\rm SU}(L^n,H)$, which is a semisimple $F$-group. I am looking for a reference where the relative system of simple roots and the conjugacy classes of $F$-parabolics in $G$ are explicitly computed. Here "relative" means with respect to a maximal split $F$-torus.

The case of a special orthogonal group is treated in Borel's 1966 paper in the Boulder collection.

I am looking for a reference where the relative root system, the relative system of simple roots, and parabolic $\Bbb R$-subgroups for the real algebraic group ${\rm SU}(p,q)$ are explicitly computed.

More generally, let $F$ be a field of characteristic 0, $L/F$ a quadratic extension, and $H$ be an $L/F$-Hermitian form on $L^n$. Write $G={\rm SU}(L^n,H)$, which is a semisimple $F$-group. I am looking for a reference where the relative system of simple roots and the conjugacy classes of $F$-parabolics in $G$ are explicitly computed. Here "relative" means with respect to a maximal split $F$-torus.

The case of a special orthogonal group is treated in Borel's 1966 paper "Linear algebraic groups" in the Boulder proceedings "Algebraic Groups and Discontinuous Subgroups", Proc. Sympos Pure Math. vol. 9. Borel writes that for an orthogonal group, the $F$-paraboics are the stabilizers of the $F$-rational isotropic flags.

Question. Is it true for $G={\rm SU}(L^n,H)$ that the $F$-parabolics in $G$ are the stabilizers of the $F$-rational isotropic flags in $(L^n, H)$ ?