Let $X$ be a smooth projective curve over $\mathbb{C}$ and Let $G$ be a complex reductive group. By a parahoric group scheme $\mathcal{G}$ over $X$, I mean a smooth group scheme over $X$ whose restriction to an open set $U$ is the constant group scheme $U \times G$ (or $\mathcal{G}_{K(X)} \cong spec(K(X)) \times G)$ and for $x \in X - U $, if $\mathcal{O}_{X,x}$ is the completion of the local ring at $x$ and $K_x$ its fraction field, then $\mathcal{G}(\mathcal{O}_{X,x}) \subset \mathcal{G}(K_x)$ is a parahoric sub-group in the sense of Bruhat-Tits. I am interested in the case when these local parahoric subgroups are just the Iwahori or the inverse image of a fixed borel subgroup $B \subset G$ under the evaluation maps ($G(\mathcal{O}_{X,x}) \rightarrow G(\mathbb{C})$). Is it true then that $$ B \subset \mathcal{G}(X)? $$ or if not is there a description of the groups $\mathcal{G}(X)$?.