Conformal blocks for Galois covers of algebraic curves
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| Format: | Preprint |
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2018
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| author | Hong, Jiuzu Kumar, Shrawan |
| author_facet | Hong, Jiuzu Kumar, Shrawan |
| contents | We study the spaces of twisted conformal blocks attached to a $Γ$-curve $Σ$ with marked $Γ$-orbits and an action of $Γ$ on a simple Lie algebra $\mathfrak{g}$, where $Γ$ is a finite group. We prove that if $Γ$ stabilizes a Borel subalgebra of $\mathfrak{g}$, then 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 $Γ$-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 Bruhat-Tits group scheme on the quotient curve $Σ/Γ$ obtained via the $Γ$-invariance of Weil restriction associated to $Σ$ 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 $Σ/Γ$ when the level $c$ is divisible by $|Γ|$ (establishing a conjecture due to Pappas-Rapoport). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1807_00118 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Conformal blocks for Galois covers of algebraic curves Hong, Jiuzu Kumar, Shrawan Group Theory Mathematical Physics Algebraic Geometry Representation Theory 17B67, 17B68, 14H81, 17B81, 14D21, 14H60, 81R10 We study the spaces of twisted conformal blocks attached to a $Γ$-curve $Σ$ with marked $Γ$-orbits and an action of $Γ$ on a simple Lie algebra $\mathfrak{g}$, where $Γ$ is a finite group. We prove that if $Γ$ stabilizes a Borel subalgebra of $\mathfrak{g}$, then 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 $Γ$-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 Bruhat-Tits group scheme on the quotient curve $Σ/Γ$ obtained via the $Γ$-invariance of Weil restriction associated to $Σ$ 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 $Σ/Γ$ when the level $c$ is divisible by $|Γ|$ (establishing a conjecture due to Pappas-Rapoport). |
| title | Conformal blocks for Galois covers of algebraic curves |
| topic | Group Theory Mathematical Physics Algebraic Geometry Representation Theory 17B67, 17B68, 14H81, 17B81, 14D21, 14H60, 81R10 |
| url | https://arxiv.org/abs/1807.00118 |