Conformal blocks for Galois covers of algebraic curves

Abstract: This is a joint work with Jiuzu Hong. We study the spaces of twisted conformal blocks attached to A-curves S with marked A-orbits and an action of A on a simple Lie algebra g, where A is a finite group. We prove that if A stabilizes a Borel subalgebra of g, then Propogation Theorem and Factorization Theorem hold. We endow a projectively flat connection on the sheaf of twisted conformal blocks attached to a smooth family of pointed A-curves; in particular, it is locally free. We also prove that the sheaf of twisted conformal blocks on the stable compactification of Hurwitz stack is locally free. We further identify the space of twisted conformal blocks with the space of global sections of certain line bundles on the stack of A-equivariant principal G-bundles over the curve S, G being the simply-connected group with Lie algebra g. This generalizes the Verlinde theory of conformal blocks to the twisted setting.