{"paper":{"title":"Multiplicity free induced representations and orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.RT","authors_text":"Maarten van Pruijssen","submitted_at":"2014-05-05T07:07:56Z","abstract_excerpt":"Let $(G,H)$ be a reductive spherical pair and $P\\subset H$ a parabolic subgroup such that $(G,P)$ is spherical. The triples $(G,H,P)$ with this property are called multiplicity free systems and they are classified in this paper. Denote by $\\pi^{H}_{\\mu}=\\mathrm{ind}_{P}^{H}\\mu$ the Borel-Weil realization of the irreducible $H$-representation of highest weight $\\mu\\in P^{+}_{H}$ and consider the induced representation $\\mathrm{ind}_{P}^{G}\\chi_{\\mu}=\\mathrm{ind}_{H}^{G}\\pi^{H}_{\\mu}$, a multiplicity free induced representation. Some properties of the spectrum of the multiplicity free induced re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0796","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"}