{"paper":{"title":"Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Markus Hunziker, William Graham","submitted_at":"2006-05-26T17:40:53Z","abstract_excerpt":"Let K be a complex reductive algebraic group and V a representation of K. Let S denote the ring of polynomials on V. Assume that the action of K on S is multiplicity free. If V_{\\lambda} is an irreducible representation of K, let S_{\\lambda} denote the corresponding isotypic component of S. Write S_{\\lambda} S_{\\mu} for the subspace of S spanned by products of S_{\\lambda} and S_{\\mu}. If V_{\\nu} occurs as an irreducible constituent of the tensor product of V_{\\lambda} and V_{\\mu}, is it true that S_{\\nu} is contained in S_{\\lambda} S_{\\mu}? We investigate this question for representations aris"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605691","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0605691/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}