Eigenfunctions of the Laplace operators for a building of type G2
Anna Maria Mantero, Anna Zappa · CINECA IRIS Institutial Research Information System (University of Genoa) · 2009
Let ∆ be a thick affine building of type ~G_2 . We prove that any eigenfunction of the Laplace operators of ∆, associated with a pair (γ_1 , γ_2 ), is the Poisson transform of a suitable finitely additive measure on the maximal boundary Ω of ∆, by using only the combinatorial structure of ∆.