{"paper":{"title":"Gelfand pairs and strong transitivity for Euclidean buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.RT","authors_text":"Corina Ciobotaru, Pierre-Emmanuel Caprace","submitted_at":"2013-04-23T09:09:47Z","abstract_excerpt":"Let G be a locally compact group acting properly by type-preserving automorphisms on a locally finite thick Euclidean building $\\Delta$ and K be the stabilizer of a special vertex in $\\Delta$. It is known that (G, K) is a Gelfand pair as soon as G acts strongly transitively on $\\Delta$; this is in particular the case when G is a semi-simple algebraic group over a local field. We show a converse to this statement, namely: if (G, K) is a Gelfand pair and G acts cocompactly on $\\Delta$, then the action is strongly transitive. The proof uses the existence of strongly regular hyperbolic elements in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6210","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}