Expanders and the Affine Building of \rm Sp_n

2007/06/15 by A. Setyadi, Setyadi, A. · 2 citations
Mathematics · #05C12 (Primary) #05C25 #51E24 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Mathematics and Applications #math.CO #msc:05C12 #msc:05C25 #msc:51E24

paper · pdf · doi:10.48550/arxiv.0706.2272

minor corrections made; 11 pages, 2 figures; to appear in Ars Combinatoria

openalex publication_date 2007/06/15 · arxiv created 2008/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For n ≥ 2 and a local field K, let Δ_n denote the affine building naturally associated to the symplectic group \rm Sp_n(K). We compute the spectral radius of the subgraph Y_n of Δ_n induced by the special vertices in Δ_n, from which it follows that Y_n is an analogue of a family of expanders and is non-amenable.

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