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

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

2007-06-15

arxiv.org/abs/0706.2272v2

Mathematics

Combinatorics

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

Scientific paper

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.

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