2011/11/30 by Sean Rostami, Rostami, Sean
Mathematics · #14G35 #14M15 #20C08 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1112.0074
openalex publication_date 2011/11/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
This paper proves that the nearby cycles complexes on a certain family of PEL\nlocal models are central with respect to the convolution product of sheaves on\nthe corresponding affine flag varieties. As a corollary, the semisimple trace\nfunctions defined using the action of Frobenius on those nearby cycles\ncomplexes are, via the sheaf-function dictionary, in the centers of the\ncorresponding Iwahori-Hecke algebras. This is commonly referred to as\nKottwitz's Conjecture. The reductive groups associated to the PEL local models\nunder consideration are unramified unitary similitude groups with even\ndimension. The proof follows the method of Haines-Ngo 2002. Upon completion of\nthe first version of this paper, Pappas and Zhu released a preprint, now\npublished, which contained within its scope the main theorem of this paper.\nHowever, the methods of Pappas-Zhu are very different and some of the proofs\nfrom this paper have been useful in forthcoming work of Haines-Stroh.\n