Folded galleries and moment graphs

2024/10/16 by Anna Reimann, Reimann, Anna
Computer Science · #20F55 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2410.12578

openalex publication_date 2024/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize folding patterns, the combinatorial options of folding minimal alcove-to-alcove galleries in affine Coxeter complexes positively with respect to Weyl chamber orientations of the Coxeter complex, by drawing a connection to the Bruhat moment graph of the associated spherical Coxeter group. We also prove how to determine the spherical direction of the end alcove of a positively folded gallery using these graphs.

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