{"paper":{"title":"Generic irreducibilty of Laplace eigenspaces on certain compact Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dorothee Schueth","submitted_at":"2016-02-15T09:55:24Z","abstract_excerpt":"If $G$ is a compact Lie group endowed with a left invariant metric $g$, then $G$ acts via pullback by isometries on each eigenspace of the associated Laplace operator $\\Delta_g$. We establish algebraic criteria for the existence of left invariant metrics $g$ on $G$ such that each eigenspace of $\\Delta_g$, regarded as the real vector space of the corresponding real eigenfunctions, is irreducible under the action of $G$. We prove that generic left invariant metrics on the Lie groups $G=\\operatorname{SU}(2)\\times\\ldots\\times\\operatorname{SU}(2)\\times T$, where $T$ is a (possibly trivial) torus, h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04602","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"}