{"paper":{"title":"Gelfand-Kirillov Dimensions of the Z-graded Oscillator Representations of $\\mathfrak{o}(n,\\mathbb{C})$ and $\\mathfrak{sp}(2n,\\mathbb{C})$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Zhanqiang Bai","submitted_at":"2015-01-20T12:33:52Z","abstract_excerpt":"In this paper, we compute the Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible $\\mathfrak{o}(n, \\mathbb{C})$-modules and $\\mathfrak{sp}(2n, \\mathbb{C})$-modules that appeared in the $\\mathbb{Z}$-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. We also found that some of the modules have the secondly minimal GK-dimension, and some of them have the larger GK-dimension than the maximal GK-dimension of unitary highest-weight modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04781","kind":"arxiv","version":2},"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"}