TY - JOUR
T1 - Conformal blocks attached to twisted groups
AU - Damiolini, Chiara
N1 - Funding Information:
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.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - 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 Hur ¯ (Γ , ξ) g,n parametrizing Γ -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.
AB - 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 Hur ¯ (Γ , ξ) g,n parametrizing Γ -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.
KW - Affine Lie algebras
KW - Galois coverings of curves
KW - Parahoric Bruhat–Tits groups
KW - Sheaves of conformal blocks
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U2 - 10.1007/s00209-019-02414-6
DO - 10.1007/s00209-019-02414-6
M3 - Article
AN - SCOPUS:85075211896
SN - 0025-5874
VL - 295
SP - 1643
EP - 1681
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3-4
ER -