{"paper":{"title":"Invariants and relative invariants under compact Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Miriam Manoel, Patricia H. Baptistelli","submitted_at":"2012-07-06T04:00:12Z","abstract_excerpt":"This paper presents algebraic methods for the study of polynomial relative invariants, when the group G formed by the symmetries and relative symmetries is a compact Lie group. We deal with the case when the subgroup H of symmetries is normal in G with index m, m greater or equal to 2. For this, we develop the invariant theory of compact Lie groups acting on complex vector spaces. This is the starting point for the study of relative invariants and the computation of their generators. We first obtain the space of the invariants under the subgroup $H$ of $\\Gamma$ as a direct sum of $m$ submodule"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1513","kind":"arxiv","version":1},"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"}