Let $K=\mathbb C((t))$ and $O=\mathbb C[[t]]$, and $n\geq 1$. Consider the matrix $$J_{2n}=\begin{pmatrix} 0& I_n \\ -I_n & 0\end{pmatrix},$$ And let $\Psi : K^{2n}\times K^{2n}\rightarrow K$ given by $$\Psi(u,v)=u\cdot J_{2n}\cdot \overline v,$$ where $\overline{f(t)}=f(-t)$.
What is the type of the group $S(\Psi)_{2n}(K)=\{g\in SL_{2n}(K); \Psi(g,g)=\Psi\}$? (as in the table given by Tits)
Is it Split? Simply connected?
Is $P=S(\Psi)_{2n}(O)$ is a maximal parahoric subgroup?
This has been studied by Pappas and Rapoport for a Hermitian $\Psi$, but I couldn't find any reference for this case.
Thanks
