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

2005/02/23 by Ulrich Goertz, Thomas J. Haines, Goertz, Ulrich +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0502499

12 pp

arxiv created 2005/02/23 · arxiv updated 2009/12/01

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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