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

Publication date: 19 February 2014

Abstract: For

n g e q 2

and a local field

K

, let

D e l t a_{n}

denote the affine building naturally associated to the symplectic group

{m S p}_{n} (K)

. We compute the spectral radius of the subgraph

Y_{n}

of

D e l t a_{n}

induced by the special vertices in

D e l t a_{n}

, from which it follows that

Y_{n}

is an analogue of a family of expanders and is non-amenable.