Let $E/F$ be a quadratic extension of number fields. If $V$ is a hermitian space over $E$, let $V=X+V_0+Y$ be its Witt decomposition, where $X,Y$ are maximal totally isotropic subspaces and $V_0$ is anisotropic kernel of $V$ respectively.

Let $P(X)$ be the parabolic subgroup of $U(V)$ stabilizing $X$. Then we can decompose $U(V)=P(X)K$ where $K$ is a maximal compact subgroup of $U(V)$.

I am wondering what is the Iwasawa decomposition of $U(V_0)$. How can we decompose it? I also want to know what is the parabolic subgroup of $U(V_0)$.

Any comments will be higly appreciated!