{"paper":{"title":"A Haagerup Inequality for $\\tA_1\\times\\tA_1$ and $\\tA_2$ Buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.FA","authors_text":"Guyan Robertson, Jacqui Ramagge, Tim Steger","submitted_at":"2013-02-22T14:08:06Z","abstract_excerpt":"Haagerup's inequality for convolvers on free groups may be interpreted as a result on $\\tA_1$ buildings, i.e. trees. Here are proved analogous inequalities for discrete groups acting freely on the vertices of $\\tA_1\\times\\tA_1$ and $\\tA_2$ buildings. The results apply in particular to groups of type-rotating automorphisms acting simply transitively on the vertices of such buildings. These results provide the first examples of higher rank groups with property (RD)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5598","kind":"arxiv","version":1},"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"}