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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.0380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-01T20:20:08Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1aeec8e124c77c8808fb4ffc03f030b1313ecda54ee1df93d3cfa54f7d9d4f2f","abstract_canon_sha256":"525eec917a30ac34bb4bf54c8d9bcf341594af6a71b8d07e8a7e760688e04142"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:25.391813Z","signature_b64":"2PGbmsWUzKQes28HtFq7YsNxfCgppUM1Mjbrtg8F8UmDCBoymfaCthVX1T8SYBdnS9ENCjt+9pnDrbp+hFurAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"570ef0e95e436237681fc73cf319b0064bc680113ce22f6f27c7e44fd1e3c550","last_reissued_at":"2026-05-18T04:05:25.391178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:25.391178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $m=\\dim(H^2(G/P))$. 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