{"paper":{"title":"Invariant connections and invariant holomorphic bundles on homogeneous manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrei Teleman, Indranil Biswas","submitted_at":"2013-05-15T11:20:54Z","abstract_excerpt":"Let $X$ be a differentiable manifold endowed with a transitive action $\\alpha:A\\times X\\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: {enumerate} equivalence classes of $\\alpha$-invariant $K$-connections on $X$,\n  $\\alpha$-invariant gauge classes of $K$-connections on $X$, and\n  $\\alpha$-invariant isomorphism classes of pairs $(Q,P)$ consisting of a holomorphic $K^\\C$-bundle $Q\\longrightarrow X$ and a $K$-reduction $P$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3430","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"}