{"paper":{"title":"Product and puzzle formulae for GL_n Belkale-Kumar coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Allen Knutson, Kevin Purbhoo","submitted_at":"2010-08-30T01:10:39Z","abstract_excerpt":"The Belkale-Kumar product on H*(G/P) is a degeneration of the usual cup product on the cohomology ring of a generalized flag manifold. In the case G=GL_n, it was used by N. Ressayre to determine the regular faces of the Littlewood-Richardson cone.\n  We show that for G/P a (d-1)-step flag manifold, each Belkale-Kumar structure constant is a product of d(d-1)/2 Littlewood-Richardson numbers, for which there are many formulae available, e.g. the puzzles of [Knutson-Tao '03]. This refines previously known factorizations into d-1 factors. We define a new family of puzzles to assemble these to give "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4979","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"}