{"paper":{"title":"A geometric quantization of the Kostant-Sekiguchi correpondence for scalar type unitary highest weight representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.RT","authors_text":"Jan M\\\"ollers","submitted_at":"2012-05-23T13:58:12Z","abstract_excerpt":"For any Hermitian Lie group $G$ of tube type we give a geometric quantization procedure of certain $K_{\\mathbb{C}}$-orbits in $\\mathfrak{p}_{\\mathbb{C}}^*$ to obtain all scalar type highest weight representations. Here $K_{\\mathbb{C}}$ is the complexification of a maximal compact subgroup $K\\subseteq G$ with corresponding Cartan decomposition $\\mathfrak{g}=\\mathfrak{k}+\\mathfrak{p}$ of the Lie algebra of $G$. We explicitly realize every such representation $\\pi$ on a Fock space consisting of square integrable holomorphic functions on its associated variety $Ass(\\pi)\\subseteq\\mathfrak{p}_{\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5171","kind":"arxiv","version":4},"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"}