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

2022/09/15 by Hong, Jiuzu, Yu, Huanhuan · 1 citation
#14H60 #14M15 #17B67 #22E46 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2209.07347

Abstract

Let G be a parahoric Bruhat-Tits group schemes arising from a Γ-curve C and a certain Γ-action on a simple algebraic group G for some finite cyclic group Γ. We prove the flatness of Beilinson-Drinfeld Schubert varieties of G, we determine the rigidified Picard group of the Beilinson-Drinfeld Grassmannian \rm Gr_G,Cⁿ of G, and we establish the factorizable and equivariant structures on rigidified line bundles on \rm Gr_G,Cⁿ. We develop an algebraic theory of global Demazure modules of twisted current algebras, and using our geometric results we prove that when C = \mathbbA¹, the spaces of global sections of line bundles on BD Schubert varieties of G are dual to the twisted global Demazure modules. This generalizes the work of Dumanski-Feigin-Finkelberg in the untwisted setting,

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