2024/05/14 by Tullio Ceccherini‐Silberstein, Ceccherini-Silberstein, Tullio, Fabio Scarabotti +3
Mathematics · #20C15 #20E22 #20G40 #33C55 #43A90 #Advanced Algebra and Geometry #Advanced Banach Space Theory #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2405.08371
openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K≤ H be two finite groups and let C≤ A be two finite abelian groups, with H acting on A as a group of isomorphisms admitting C as a K-invariant subgroup. We study the homogeneous space X\coloneqq(H\ltimes A)/(K\ltimes C) and determine the decomposition of the permutation representation of H\ltimes A acting on X. We then characterize when this is multiplicity-free, that is, when (H\ltimes A,K\ltimes C) is a Gelfand pair. If this is the case, we explicitly calculate the corresponding spherical functions. From our general construction and related analysis, we recover Dunkl's results on the q-analog of the nonbinary Johnson scheme.