A Hitchin connection on non abelian theta functions for parabolic G-bundles

Abstract

For a simple, simply connected, complex group G, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points.

arXiv commentFinal version: To appear in Crelle's Journal. Major Changes based on comments of anonymous referees: Section on Ginzburg algebra is split from this to form a separate paper, Theorem 6.3 from arXiv2110.00430v1 (also will be updated soon) is now moved to this paper with additional details