Connections on Parahoric Torsors over Curves

Abstract

We define parahoric g-torsors for a certain class of Bruhat-Tits group schemes g on a smooth complex projective curve X when the weights are real, and also define connections on them. We prove that a g-torsor is given by a homomorphism from π1(X\D) to a maximal compact subgroup of G, where the finite subset D ⊂ X is the parabolic divisor, if and only if the G-torsor is polystable.