{"paper":{"title":"Geometric Quantization of Real Minimal Nilpotent Orbits","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.SG","authors_text":"Ranee Brylinski","submitted_at":"1998-11-06T04:10:34Z","abstract_excerpt":"In this paper, we begin a quantization program for nilpotent orbits of a real semisimple Lie group. These orbits and their covers generalize the symplectic vector space.\n A complex structure polarizing the orbit and invariant under a maximal compact subgroup is provided by the Kronheimer-Vergne Kaehler structure. We outline a geometric program for quantizing the orbit with respect to this polarization.\n We work out this program in detail for minimal nilpotent orbits in the non-Hermitian case. The Hilbert space of quantization consists of holomorphic half-forms on the orbit. We construct the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9811033","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"}