Opérateurs invariants sur un immeuble affine de type $widetilde B_n$ (n>=3)

International audienceWe consider a building ∆ of type $widetilde B_n$ (n ≥ 3), different subsets S′ of the set S of vertices in ∆ and an automorphism group G strongly transitive and type preserving on ∆. We prove that the algebra of G-invariant operators acting on the space of functions on S′ is not commutative (contrarily to the classical results) and we give its generators. We give also the precise structure of some commutative subalgebra