JournalsrsmupVol. 127pp. 75–98

Opérateurs invariants sur un immeuble affine de type B~n(n3)\tilde B_n (n\ge3)

  • Ferdaous Kellil

    ISIMM, Université de Monastir, Tunisia
  • Guy Rousseau

    Université de Lorraine, Vandoeuvre lès Nancy, France
Opérateurs invariants sur un immeuble affine de type $\tilde B_n (n\ge3)$ cover
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Abstract

We consider a building Δ\Delta of type \widetilde{B}_n~(n\geq 3), different subsets S\mathcal{S}' of the set S\mathcal{S} of vertices in Δ\Delta and an automorphism group GG strongly transitive and type preserving on Δ\Delta. We prove that the algebra of GG-invariant operators acting on the space of functions on S\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.

Cite this article

Ferdaous Kellil, Guy Rousseau, Opérateurs invariants sur un immeuble affine de type B~n(n3)\tilde B_n (n\ge3). Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 75–98

DOI 10.4171/RSMUP/127-5