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Bounds on weights of nearby cycles and Wakimoto sheaves on affine flag manifolds

Ulrich Goertz·Thomas J. Haines
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Abstract

We study certain nearby cycles sheaves on an affine flag manifold which arise naturally in the Beilinson-Gaitsgory deformation of the affine flag manifold to the affine Grassmannian. We study the multiplicity functions we introduced in an earlier paper, which encode the data of the Jordan-Hoelder series. We prove the multiplicity functions are polynomials in q, and we give a sharp bound for their degrees. Our results apply as well to the nearby cycles in the p-adic deformation of Laumon-Haines-Ngo, and also to Wakimoto sheaves.

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Ulrich Goertz, Thomas J. Haines. 2005-02-23. Bounds on weights of nearby cycles and Wakimoto sheaves on affine flag manifolds. https://arxiv.org/abs/math/0502499

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