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

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

2005-02-23

arxiv.org/abs/math/0502499v1

Mathematics

Algebraic Geometry

12 pp

Scientific paper

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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