Expanders and the Affine Building of ${\rm Sp}_n$
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2007
- DOI:
- 10.48550/arXiv.0706.2272
- arXiv:
- arXiv:0706.2272
- Bibcode:
- 2007arXiv0706.2272S
- Keywords:
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- Mathematics - Combinatorics;
- 05C12 (Primary);
- 05C25;
- 51E24 (Secondary)
- E-Print:
- minor corrections made