{"paper":{"title":"Category O over a deformation of the symplectic oscillator algebra","license":"","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Apoorva Khare","submitted_at":"2003-09-15T21:29:04Z","abstract_excerpt":"We discuss the representation theory of $H_f$, which is a deformation of the symplectic oscillator algebra $sp(2n) \\ltimes h_n$, where $h_n$ is the ((2n+1)-dimensional) Heisenberg algebra. We first look at a more general setup, involving an algebra with a triangular decomposition. Assuming the PBW theorem, and one other hypothesis, we show that the BGG category $\\mathcal{O}$ is abelian, finite length, and self-dual.\n  We decompose $\\mathcal{O}$ as a direct sum of blocks $\\calo(\\la)$, and show that each block is a highest weight category.\n  In the second part, we focus on the case $H_f$ for $n="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309251","kind":"arxiv","version":3},"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"}