{"paper":{"title":"Representations of The Coordinate Ring of $GL_{q}(3)$","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Vahid Karimipour","submitted_at":"1993-05-19T15:06:15Z","abstract_excerpt":"It is shown that the finite dimensional ireducible representations of the quantum matrix algebra $ M_q(3) $ ( the coordinate ring of $ GL_q(3) $ ) exist only when q is a root of unity ( $ q^p = 1 $ ). The dimensions of these representations can only be one of the following values: $ p^3 , { p^3 \\over 2 } , { p^3 \\over 4 } $ or $ { p^3 \\over 8 } $ . The topology of the space of states ranges between two extremes , from a 3-dimensional torus $ S^1 \\times S^1 \\times S^1 $ ( which may be thought of as a generalization of the cyclic representation ) to a 3-dimensional cube $ [ 0 , 1 ]\\times [ 0 , 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9305085","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"}