Expanders and the Affine Building of ${\rm Sp}_n$

A. Setyadi

Expanders and the Affine Building of ${\rm Sp}_n$

Combinatorics 2008-03-04 v2

Authors: A. Setyadi

Abstract

For $n \geq 2$ and a local field $K$ , let $\Delta_n$ 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 $\Delta_n$ induced by the special vertices in $\Delta_n$ , from which it follows that $Y_n$ is an analogue of a family of expanders and is non-amenable.

Keywords

expanders affine building symplectic group spectral radius local field non-amenable special vertices

Cite

@article{arxiv.0706.2272,
  title  = {Expanders and the Affine Building of ${\rm Sp}_n$},
  author = {A. Setyadi},
  journal= {arXiv preprint arXiv:0706.2272},
  year   = {2008}
}

Comments

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

Expanders and the Affine Building of ${\rm Sp}_n$

Abstract

Keywords

Cite

Comments

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