{"paper":{"title":"Action of complex Symplectic matrices on the Siegel upper half space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Keshav Raj Acharya, Matt McBride","submitted_at":"2017-11-21T12:36:07Z","abstract_excerpt":"The Siegel upper half space, $\\mathcal{S}_n$, the space of complex symmetric matrices, $Z$ with positive definite imaginary part, is the generalization of the complex upper half plane in higher dimensions. In this paper, we study a generalization of linear fractional transformations, $\\Phi_S$, where $S$ is a complex symplectic matrix, on the Siegel upper half space. We partially classify the complex symplectic matrices for which $\\Phi_S(Z)$ is well defined. We also consider $\\mathcal S_n$ and $\\overline{\\mathcal S}_n$ as metric spaces and discuss distance properties of the map $\\Phi_S$ from $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07747","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"}