{"paper":{"title":"Bergman representative coordinates on the Siegel-Jacobi disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Stefan Berceanu","submitted_at":"2014-09-01T11:26:33Z","abstract_excerpt":"We underline some differences between the geometric aspect of Berezin's approach to quantization on homogeneous K\\\"ahler manifolds and Bergman's construction for bounded domains in $\\mathbb{C}^n$. We construct explicitly the Bergman representative coordinates for the Siegel-Jacobi disk $\\mathcal{D}^J_1$, which is a partially bounded manifold whose points belong to $\\mathbb{C}\\times\\mathcal{D}_1$, where $\\mathcal{D}_1$ denotes the Siegel disk. The Bergman representative coordinates on $\\mathcal{D}^J_1$ are globally defined, the Siegel-Jacobi disk is a normal K\\\"ahler homogeneous Lu Qi-Keng mani"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0368","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"}