{"paper":{"title":"Cohomological equation and cocycle rigidity of parabolic actions in $SL(n,\\RR)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DS","authors_text":"Zhenqi Jenny Wang","submitted_at":"2012-11-05T07:10:20Z","abstract_excerpt":"For any unitary representation $(\\pi,\\mathcal{H})$ of $G=SL(n,\\RR)$, $n\\geq 3$ without non-trivial $G$-invariant vectors, we study smooth solutions of the cohomological equation $\\mathfrak{u}f=g$ where $\\mathfrak{u}$ is a vector in the root space of $\\mathfrak{sl}(n,\\RR)$ and $g$ is a given vector in $\\mathcal{H}$. We characterize the obstructions to solving the cohomological equation, construct smooth solutions of the cohomological equation and obtain tame Sobolev estimates for $f$.\n  We also study common solutions to (the infinitesimal version of) the cocycle equation $\\mathfrak{u}h=\\mathfra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0777","kind":"arxiv","version":3},"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"}