Alcove walks and nearby cycles on affine flag manifolds

2006/10/27 by Ulrich Goertz, Goertz, Ulrich
Mathematics · #20C08 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0610839

openalex publication_date 2006/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using Ram's theory of alcove walks, we give a proof of the Bernstein presentation of the affine Hecke algebra. The method works also in the case of unequal parameters. We also discuss how these results help in studying sheaves of nearby cycles on affine flag manifolds.

Related

• Alcove Walks and GKM Theory for Affine Flags
• Combinatorics in affine flag varieties
• Higher nearby cycles and central sheaves on affine flag varieties
• Bounds on weights of nearby cycles and Wakimoto sheaves on affine flag manifolds
• On J-folded alcove paths and combinatorial representations of affine Hecke algebras