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Conformal blocks attached to twisted groups
Mathematische Zeitschrift ( IF 0.8 ) Pub Date : 2019-11-13 , DOI: 10.1007/s00209-019-02414-6
Chiara Damiolini

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 $${\overline{{\mathcal {H}}\text {ur}}(\Gamma ,\xi )_{g, n}}$$ H ur ¯ ( Γ , ξ ) g , n parametrizing $$\Gamma $$ 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.

中文翻译:

连接到扭曲组的共形块

本文的目的是将共形块的概念推广到以下情况:根据曲线的覆盖数据,将它们所附的李代数替换为一组李代数。结果是堆栈上有限秩的向量束 $${\overline{{\mathcal {H}}\text {ur}}(\Gamma ,\xi )_{g, n}}$$ H ur ¯ ( Γ , ξ ) g , n 参数化 $$\Gamma $$ Γ - 曲线覆盖。保形块的经典滑轮的许多特征在这个更一般的设置中被证明是成立的,特别是分解规则、真空的传播和 WZW 连接。
更新日期:2019-11-13
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