Invariant operators on an affine building of type \(\widetilde {B}_n (n\geq 3)\) (Q442629)

Summary: We consider a building \(\Delta\) of type \(\widetilde B_n\) \((n\geq 3)\), different subsets \({\mathcal S}'\) of the set \({\mathcal S}\) of vertices in \(\Delta\) and an automorphism group \(G\) strongly transitive and type preserving on \(\Delta\). We prove that the algebra of \(G\)-invariant operators acting on the space of functions on \({\mathcal S}'\) is not commutative (contrarily to the classical results) and we give its generators. We give also the precise structure of some commutative subalgebras.