Conformal blocks attached to twisted groups

  • Chiara DamioliniEmail author


The aim of this paper is to generalize the notion of conformal blocks to the situation in which the Lie algebra they are attached to is replaced with a sheaf of Lie algebras depending on covering data of curves. The result is a vector bundle of finite rank on the stack \({\overline{{\mathcal {H}}\text {ur}}(\Gamma ,\xi )_{g, n}}\) parametrizing \(\Gamma \)-coverings of curves. Many features of the classical sheaves of conformal blocks are proved to hold in this more general setting, in particular the factorization rules, the propagation of vacua and the WZW connection.


Sheaves of conformal blocks Galois coverings of curves Parahoric Bruhat–Tits groups Affine Lie algebras 

Mathematics Subject Classification

14D20 14H10 17B67 



The main results of this paper are part of my Ph.D. thesis, which was written in 2017 at the Universität Duisburg-Essen under the supervision of Jochen Heinloth. I am indebted to him for the constant support, for the useful discussions and comments on a preliminary version of this manuscript. Many thanks to Christian Pauly and Angela Gibney. I am grateful to the anonymous referee for their comments and suggestions.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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