The extremal symmetry of arithmetic simplicial complexes

الأصل · EN

Let G be a higher-rank semisimple Lie group over a nonarchimedean local field, for example G= PGL(n,Qₚ). To any lattice L in G there is an associated simplicial complex Bₗ, given by the quotient by L of the Bruhat-Tits building associated to G. In this paper prove that the simplicial structure Bₗ exhibits some remarkable and extremal symmetry properties, in particular when compared to any other simplicial structure on (any cover of) Bₗ.