Title: Connections on parahoric torsors over curves,
Abstract: We define parahoric $\cG$--torsors for certain Bruhat--Tits group scheme
$\cG$ on a smooth complex projective curve $X$ when the weights are real, and
also define connections on them. We prove that a $\cG$--torsor is given by a
homomorphism from $\pi_1(X\setminus D)$ to a maximal compact subgroup of $G$,
where $D\, \subset\, X$ is the parabolic divisor, if and only if the torsor is
polystable.