{"paper":{"title":"Symmetric quivers, invariant theory, and saturation theorems for the classical groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Steven V Sam","submitted_at":"2010-09-15T21:07:29Z","abstract_excerpt":"Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \\lambda^1, ..., \\lambda^r such that the tensor product V_{N\\lambda^1} \\otimes ... \\otimes V_{N\\lambda^r} contains nonzero G-invariants for some N \\ge 1, we show that the tensor product V_{2\\lambda^1} \\otimes ... \\otimes V_{2\\lambda^r} also contains nonzero G-invariants. This extends results of Kapovich-Millson and Belkale-Kumar and complements similar results for the general linear group due to Knutson-Tao and Derksen-Weym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3040","kind":"arxiv","version":2},"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"}