%AHong, Jiuzu%AKumar, Shrawan%BJournal Name: Compositio Mathematica; Journal Volume: 159; Journal Issue: 10
%D2023%ICambridge University Press
%JJournal Name: Compositio Mathematica; Journal Volume: 159; Journal Issue: 10
%K
%MOSTI ID: 10519991
%PMedium: X
%TConformal blocks for Galois covers of algebraic curves
%XWe study the spaces of twisted conformal blocks attached to a$\Gamma$-curve$\Sigma$with marked$\Gamma$-orbits and an action of$\Gamma$on a simple Lie algebra$\mathfrak {g}$, where$\Gamma$is a finite group. We prove that if$\Gamma$stabilizes a Borel subalgebra of$\mathfrak {g}$, then the propagation theorem and factorization theorem hold. We endow a flat projective connection on the sheaf of twisted conformal blocks attached to a smooth family of pointed$\Gamma$-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. Let$\mathscr {G}$be the parahoric Bruhatâ€“Tits group scheme on the quotient curve$\Sigma /\Gamma$obtained via the$\Gamma$-invariance of Weil restriction associated to$\Sigma$and the simply connected simple algebraic group$G$with Lie algebra$\mathfrak {g}$. We prove that the space of twisted conformal blocks can be identified with the space of generalized theta functions on the moduli stack of quasi-parabolic$\mathscr {G}$-torsors on$\Sigma /\Gamma$when the level$c$is divisible by$|\Gamma |$(establishing a conjecture due to Pappas and Rapoport).

%0Journal Article