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arXiv · 2412.15062

A refinement of the coherence conjecture of Pappas and Rapoport

Jiuzu Hong·Huanhuan Yu
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Abstract

The coherence conjecture of Pappas and Rapoport, proved by Zhu, asserts the equality of dimensions for the global sections of a line bundle over a spherical Schubert variety in the affine Grassmannian and those of another line bundle over a certain union of Schubert varieties in a partial affine flag variety. We refine this equality of dimensions to an isomorphism of representations. The comparison is established by introducing a parahoric Bruhat-Tits group scheme $\mathcal{G}$ over the affine line, ramified at 0. We further strengthen this comparison by equipping any line bundle on the global Schubert variety of $\mathcal{G}$ with a unique equivariant structure under the global jet group scheme. As an application, we obtain new relations among affine Demazure modules.

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Jiuzu Hong, Huanhuan Yu. 2026-09-21. A refinement of the coherence conjecture of Pappas and Rapoport. https://arxiv.org/abs/2412.15062

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