Rendiconti del Seminario Matematico della Università di Padova

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Volume 127, 2012, pp. 75–98
DOI: 10.4171/RSMUP/127-5

Opérateurs invariants sur un immeuble affine de type $\tilde B_n (n\ge3)$

Ferdaous Kellil[1] and Guy Rousseau[2]

(1) Département de Mathématiques, ISIMM, Université de Monastir, 5000, Monastir, Tunisia
(2) Institut Elie Cartan, Université de Lorraine, CNRS, Boulevard des aiguillettes, BP 70239, 54506, Vandœuvre-lès-Nancy, France

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.

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Kellil Ferdaous, Rousseau Guy: Opérateurs invariants sur un immeuble affine de type $\tilde B_n (n\ge3)$. Rend. Sem. Mat. Univ. Padova 127 (2012), 75-98. doi: 10.4171/RSMUP/127-5