Bounds on Weights of Nearby Cycles and Wakimoto Sheaves on Affine Flag Manifolds
- 52 Downloads
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-Hölder 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–Ngô, and also to Wakimoto sheaves.
KeywordsCoxeter Group Bruhat Order Bernstein Function Multiplicity Function Perverse Sheave
Unable to display preview. Download preview PDF.
- 1.Arkhipov S., Bezrukavnikov R. (2002) Perverse sheaves on affine flags and Langlands dual group, Preprint math.RT/0201073Google Scholar
- 3.Beilinson A., Bernstein I.N., Deligne P.: Faisceaux pervers. Astérisque 100, (1981)Google Scholar
- 6.Görtz U., Haines T.: The Jordan-Hölder series for nearby cycles on some Shimura varieties and affine flag varieties. J. Reine. Angew. Math. (to appear), math.AG/0402143Google Scholar
- 12.Kiehl R., Weissauer R. (2001) Weil conjectures, perverse sheaves and ℓ-adic Fourier transform, Springer Erg. Math. 3. Folge, 42 Google Scholar