{"paper":{"title":"The relative Hochschild-Serre spectral sequence and the Belkale-Kumar product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Sam Evens, William Graham","submitted_at":"2012-01-01T20:20:08Z","abstract_excerpt":"We consider the Belkale-Kumar cup product $\\odot_t$ on $H^*(G/P)$ for a generalized flag variety $G/P$ with parameter $t \\in \\C^m$, where $m=\\dim(H^2(G/P))$. For each $t\\in \\C^m$, we define an associated parabolic subgroup $P_K \\supset P$. We show that the ring $(H^*(G/P), \\odot_t)$ contains a graded subalgebra $A$ isomorphic to $H^*(P_K/P)$ with the usual cup product, where $P_K$ is a parabolic subgroup associated to the parameter $t$. Further, we prove that $(H^*(G/P_K), \\odot_0)$ is the quotient of the ring $(H^*(G/P), \\odot_t)$ with respect to the ideal generated by elements of positive de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0380","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"}