{"paper":{"title":"Eichler-Shimura isomorphism for complex hyperbolic lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.GT","authors_text":"Genkai Zhang, Inkang Kim","submitted_at":"2013-03-01T03:42:17Z","abstract_excerpt":"We consider the cohomology group $H^1(\\Gamma, \\rho)$ of a discrete subgroup $\\Gamma\\subset G=SU(n, 1)$ and the symmetric tensor representation $\\rho$ on $S^m(\\mathbb C^{n+1})$.\n  We give an elementary proof of the Eichler-Shimura isomorphism that harmonic forms $H^1(\\Gamma\\backslash G/K, \\rho)$ are $(0, 1)$-forms for the automorphic holomorphic bundle induced by the representation $S^m(\\mathbb C^{n})$ of $K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0074","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"}