{"paper":{"title":"Gelfand-Kirillov Dimensions of Highest Weight Harish-Chandra Modules for $SU(p,q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Xun Xie, Zhanqiang Bai","submitted_at":"2017-07-09T11:49:15Z","abstract_excerpt":"Let $ (G,K) $ be an irreducible Hermitian symmetric pair of non-compact type with $G=SU(p,q)$, and let $ \\lambda $ be an integral weight such that the simple highest weight module $ L(\\lambda) $ is a Harish-Chandra $ (\\mathfrak{g},K) $-module. We give a combinatoric algorithm for the Gelfand-Kirillov dimension of $ L(\\lambda) $. This enables us to prove that the Gelfand-Kirillov dimension of $ L(\\lambda) $ decreases as the integer $ \\langle\\lambda+\\rho,\\beta^\\vee\\rangle $ increases, where $\\rho$ is the half sum of positive roots and $\\beta$ is the maximal noncompact root. As a byproduct, we ob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02565","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"}