{"paper":{"title":"Non-vanishing cohomology classes in uniform lattices of $\\text{SO}(n,\\mathbb{H})$ and automorphic representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Arghya Mondal, Parameswaran Sankaran","submitted_at":"2016-10-05T11:35:17Z","abstract_excerpt":"Let $X$ denote the non-compact globally Hermitian symmetric space of type $DIII$, namely, $\\text{SO}(n,\\mathbb{H})/\\text{U}(n)$. Let $\\Lambda$ be a uniform torsionless lattice in $\\text{SO}(n,\\mathbb{H})$. In this note we construct certain complex analytic submanifolds in the locally symmetric space $X_\\Gamma:=\\Gamma\\backslash \\text{SO}(n,\\mathbb{H})/\\text{U}(n)$ for certain finite index sub lattices $\\Gamma\\subset \\Lambda$ and show that their dual cohomology classes in $H^*(X_\\Gamma;\\mathbb{C})$ are not in the image of the Matsushima homomorphism $H^*(X_u; \\mathbb{C})\\to H^*(X_\\Gamma;\\mathbb{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01368","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"}