The paper refines Zhu's proof of the Pappas-Rapoport coherence conjecture from an equality of dimensions to isomorphisms of representations, with applications to affine Demazure modules.
Picard group of connected affine algebraic group
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abstract
We prove that the Picard group of a connected affine algebraic group $G$ is isomorphic to the fundamental group of the derived subgroup of the reductive algebraic group $G/{\mathscr R}_u(G)$, where ${\mathscr R}_u(G)$ is the unipotent radical of $G$.
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A refinement of the coherence conjecture of Pappas and Rapoport
The paper refines Zhu's proof of the Pappas-Rapoport coherence conjecture from an equality of dimensions to isomorphisms of representations, with applications to affine Demazure modules.