{"paper":{"title":"Hausdorffness for Lie algebra homology of Schwartz spaces and applications to the comparison conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Avraham Aizenbud, Bernhard Kr\\\"otz, Dmitry Gourevitch, Gang Liu","submitted_at":"2014-03-24T11:28:07Z","abstract_excerpt":"Let $H$ be a real algebraic group acting equivariantly with finitely many orbits on a real algebraic manifold $X$ and a real algebraic bundle $\\mathcal{E}$ on $X$. Let $\\mathfrak{h}$ be the Lie algebra of $H$. Let $\\mathcal{S}(X,\\mathcal{E})$ be the space of Schwartz sections of $\\mathcal{E}$. We prove that $\\mathfrak{h}\\mathcal{S}(X,\\mathcal{E})$ is a closed subspace of $\\mathcal{S}(X,\\mathcal{E})$ of finite codimension.\n  We give an application of this result in the case when $H$ is a real spherical subgroup of a real reductive group $G$. We deduce an equivalence of two old conjectures due t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5917","kind":"arxiv","version":4},"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"}