Beilinson-Drinfeld Schubert varieties of parahoric group schemes and twisted global Demazure modules

Abstract

Let $\mathcal{G}$ be a parahoric Bruhat-Tits group schemes arising from a $\Gamma$-curve $C$ and a certain $\Gamma$-action on a simple algebraic group $G$ for some finite cyclic group $\Gamma$. We prove the flatness of Beilinson-Drinfeld Schubert varieties of $\mathcal{G}$, we determine the rigidified Picard group of the Beilinson-Drinfeld Grassmannian ${\mathrm{Gr}}_{\mathcal{G},C^n}$ of $\mathcal{G}$, and we establish the factorizable and equivariant structures on rigidified line bundles on ${\mathrm{Gr}}_{\mathcal{G},C^n}$. We develop an algebraic theory of global Demazure modules of twisted current algebras, and using our geometric results we prove that when $C={\mathbb{A}}^1$, the spaces of global sections of line bundles on BD Schubert varieties of $\mathcal{G}$ are dual to the twisted global Demazure modules. This generalizes the work of Dumanski-Feigin-Finkelberg in the untwisted setting,

arXiv comment70pages. To appear in Selecta Mathematica

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Cited by in corpus (1)

• Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules