Shadows in the wild -- folded galleries and their applications

2021/09/06 by Petra Schwer, Schwer, Petra
Mathematics · #05E10 #05E45 #11G25 (Primary) #14L05 (Secondary) #14M15 #20E42 #20F55 #20G25 #51E24 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #History and Overview (math.HO) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2109.02293

openalex publication_date 2021/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This survey is about combinatorial objects related to reflection groups and their applications in representation theory and arithmetic geometry. Coxeter groups and folded galleries in Coxeter complexes are introduced in detail and illustrated by examples. Further it is explained how they relate to retractions in Bruhat-Tits buildings and to the geometry of affine flag varieties and affine Grassmannians. The goal is to make these topics accessible to a wide audience.

Related

• Folded galleries and moment graphs
• Sketches, moves and partitions: counting regions of deformations of reflection arrangements
• A gallery model for affine flag varieties via chimney retractions
• Generalized Dynkin diagrams and root systems and their folding
• Reflection groups in algebraic geometry