{"paper":{"title":"The moment map on symplectic vector space and oscillator representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Takashi Hashimoto","submitted_at":"2014-08-28T00:09:33Z","abstract_excerpt":"The aim of this paper is to show that the canonical quantization of the moment maps on symplectic vector spaces naturally gives rise to the oscillator representations. More precisely, let $(W,\\omega)$ denote a real symplectic vector space, on which a Lie group $G$ acts symplectically on the left, where $G$ denotes a real reductive Lie group $\\mathrm{Sp}(n,\\mathbb R), \\mathrm U(p,q)$ or $\\mathrm O^*(2n)$ in this paper. Then we quantize the moment map $\\mu: W \\to \\mathfrak g_0^*$, where $\\mathfrak g_0^*$ denotes the dual space of the Lie algebra $\\mathfrak g_0$ of $G$. Namely, after taking a com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6597","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"}