Opérateurs invariants sur certains immeubles affines de rang 2
Résumé
We consider a building $\Delta$ of type $\widetilde A_2$ or $\widetilde B_2$, different subsets $S'$ of vertices in $\Delta$ and different automorphism groups $G$, very strongly transitive on $\Delta$. We prove that the algebra of $G-$invariant operators acting on the space of functions on $S'$ is often not commutative (contrarily to the classical results). In some cases we describe its structure, determine its radial eigenfunctions and deduce that the Helgason conjecture (about the Poisson transform) is not verified in this context.
Domaines
Théorie des groupes [math.GR]
Fichier principal
_05b2_Operateurs_invariants_sur_certains_immeubles_de_rang_2_F.Kellil-G.R_.pdf (227.46 Ko)
Télécharger le fichier
Loading...