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We view the (quantum) cohomology of these Grassmannians as endowed simultaneously with two structures, one of a module over the algebra of symmetric functions, and the other, of a module over the Langlands dual Lie algebra, and investigate the interaction between the two. In particular, we stu"},"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":"1106.3120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-15T23:30:07Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"298cca6b0026e0542c3b409aadb3e6999798adccac9146b608aaf42e467fa1fe","abstract_canon_sha256":"f3e48e959e7afa31b22d6b7cf67365e64b184ce32cc3be634c06db6a2f721056"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:54.180922Z","signature_b64":"WtgTqUKB+6YFYcvQxkCRG57GfSbaQgy3Wsmv6SxvRcVn9fd1jTyMuqLuS38WUFB+pguJTol7lruPTS23ZtTmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbc93c02b82e3d971567d8453c03e54cf10c72b27a60c3814f30a26f4488168d","last_reissued_at":"2026-05-18T04:19:54.180252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:54.180252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum cohomology and the Satake isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AG","authors_text":"L. Manivel, V. Golyshev","submitted_at":"2011-06-15T23:30:07Z","abstract_excerpt":"We prove that the geometric Satake correspondence admits quantum corrections for minuscule Grassmannians of Dynkin types $A$ and $D$. We find, as a corollary, that the quantum connection of a spinor variety $OG(n,2n)$ can be obtained as the half-spinorial representation of that of the quadric $Q_{2n-2}$. We view the (quantum) cohomology of these Grassmannians as endowed simultaneously with two structures, one of a module over the algebra of symmetric functions, and the other, of a module over the Langlands dual Lie algebra, and investigate the interaction between the two. 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