{"paper":{"title":"Quadratic independence of coordinate functions of certain homogeneous spaces and action of compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.QA","authors_text":"Debashish Goswami","submitted_at":"2011-06-25T06:57:01Z","abstract_excerpt":"Let $G$ be one of the classical compact, simple, centre-less, connected Lie groups or rank $n$ with a maximal torus $T$, the Lie algebra $\\clg$ and let $\\{ E_i, F_i, H_i, i=1, \\ldots, n \\}$ be the standard set of generators corresponding to a basis of the root system. Consider the adjoint-orbit space $M=\\{ {\\rm Ad}_g(H_1),~g \\in G \\}$, identified with the homogeneous space $G/L$ where $L=\\{ g \\in G:~{\\rm Ad}_g(H_1)=H_1\\}$. We prove that the `coordinate functions' $\\{ f_i, i=1, \\ldots, n \\}$, (where $f_i(g):=\\lambda_i({\\rm Ad}_g(H_1))$, $\\{ \\lambda_1, \\ldots, \\lambda_n\\}$ is basis of $\\clg^\\pri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5107","kind":"arxiv","version":6},"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"}