Gelfand pairs and strong transitivity for Euclidean buildings

DOI10.1017/etds.2013.102zbMath1355.37047arXiv1304.6210OpenAlexW3098070170MaRDI QIDQ5262256

Corina Ciobotaru, Pierre-Emmanuel Caprace

Publication date: 13 July 2015

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.6210

zbMATH Keywords

locally compact groupGelfand pair

Mathematics Subject Classification ID

Automorphism groups of locally compact groups (22D45) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Compact groups (22C05) Group algebras of locally compact groups (22D15)

Related Items (14)

Infinitely generated Hecke algebras with infinite presentation ⋮ Invariant random subgroups over non-Archimedean local fields ⋮ Gelfand pairs admit an Iwasawa decomposition ⋮ Locally compact groups with every isometric action bounded or proper ⋮ Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings ⋮ The flat closing problem for buildings ⋮ CHABAUTY LIMITS OF SIMPLE GROUPS ACTING ON TREES ⋮ A homogeneous \({\tilde{A}}_2\)-building with a non-discrete automorphism group is Bruhat-Tits ⋮ Chabauty limits of parahoric subgroups of \(\mathrm{SL}(n,\mathbb{Q}_p)\) ⋮ Distance regularity in buildings and structure constants in Hecke algebras ⋮ The cone topology on masures. With an appendix by Auguste Hébert (Université de Lyon) ⋮ Chabauty limits of diagonal Cartan subgroups of \(\mathrm{SL}(n, \mathbb{Q}_p)\) ⋮ Some remarks on proper actions, proper metric spaces, and buildings ⋮ Strongly transitive actions on Euclidean buildings

Cites Work

• Hyperbolic configurations of roots and Hecke algebras
• Analyse harmonique dans les systèmes de Tits bornologiques de type affine
• Orbihedra of nonpositive curvature
• About affine Anosov diffeomorphisms with differentiable stable and instable foliations
• Fixed points and amenability in non-positive curvature
• A classification of commutative parabolic Hecke algebras.
• Buildings and Hecke algebras.
• Cartan subgroups and lattices in semi-simple groups
• A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
• Isometry groups of non-positively curved spaces: structure theory
• Buildings
• Groups acting on trees: From local to global structure

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