{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ND35BVDQYCWQQC7KBD6MBW47NC","short_pith_number":"pith:ND35BVDQ","schema_version":"1.0","canonical_sha256":"68f7d0d470c0ad080bea08fcc0db9f68a9c8a91a8fd22b14d05e10f86178062a","source":{"kind":"arxiv","id":"1509.00112","version":3},"attestation_state":"computed","paper":{"title":"Quantum K-theoretic geometric Satake","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Joel Kamnitzer, Sabin Cautis","submitted_at":"2015-09-01T01:40:42Z","abstract_excerpt":"The geometric Satake correspondence gives an equivalence of categories between the representations of a semisimple group $ G $ and the spherical perverse sheaves on the affine Grassmannian $Gr$ of its Langlands dual group. Bezrukavnikov-Finkelberg developed a derived version of this equivalence which relates the derived category of $ G^\\vee$-equivariant constructible sheaves on $ Gr $ with the category of $G$-equivariant ${\\mathcal O}(\\mathfrak g)$-modules.\n  In this paper, we develop a K-theoretic version of the derived geometric Satake which involves the quantum group $ U_q \\mathfrak g $. We"},"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":"1509.00112","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-01T01:40:42Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"084d16ab746b86ec832d9c4ba7469b6702817297fc7b953d6dbf916ea861a5e9","abstract_canon_sha256":"305fa59bdf97a033132c3db32aaabcf565b58c83c012cf28cd34b8e012597aab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.395923Z","signature_b64":"Q1ieCf5FeUUi5Bn6dIvdQxzHpt7Ugb0FjsfP0plT6WH9eicQ9cHv9lW/sr86HS8hHskyVZ8J50AUFqzwGq9QDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68f7d0d470c0ad080bea08fcc0db9f68a9c8a91a8fd22b14d05e10f86178062a","last_reissued_at":"2026-05-17T23:53:34.395187Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.395187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum K-theoretic geometric Satake","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Joel Kamnitzer, Sabin Cautis","submitted_at":"2015-09-01T01:40:42Z","abstract_excerpt":"The geometric Satake correspondence gives an equivalence of categories between the representations of a semisimple group $ G $ and the spherical perverse sheaves on the affine Grassmannian $Gr$ of its Langlands dual group. Bezrukavnikov-Finkelberg developed a derived version of this equivalence which relates the derived category of $ G^\\vee$-equivariant constructible sheaves on $ Gr $ with the category of $G$-equivariant ${\\mathcal O}(\\mathfrak g)$-modules.\n  In this paper, we develop a K-theoretic version of the derived geometric Satake which involves the quantum group $ U_q \\mathfrak g $. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00112","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.00112","created_at":"2026-05-17T23:53:34.395285+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.00112v3","created_at":"2026-05-17T23:53:34.395285+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00112","created_at":"2026-05-17T23:53:34.395285+00:00"},{"alias_kind":"pith_short_12","alias_value":"ND35BVDQYCWQ","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"ND35BVDQYCWQQC7K","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"ND35BVDQ","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC","json":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC.json","graph_json":"https://pith.science/api/pith-number/ND35BVDQYCWQQC7KBD6MBW47NC/graph.json","events_json":"https://pith.science/api/pith-number/ND35BVDQYCWQQC7KBD6MBW47NC/events.json","paper":"https://pith.science/paper/ND35BVDQ"},"agent_actions":{"view_html":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC","download_json":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC.json","view_paper":"https://pith.science/paper/ND35BVDQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.00112&json=true","fetch_graph":"https://pith.science/api/pith-number/ND35BVDQYCWQQC7KBD6MBW47NC/graph.json","fetch_events":"https://pith.science/api/pith-number/ND35BVDQYCWQQC7KBD6MBW47NC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC/action/storage_attestation","attest_author":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC/action/author_attestation","sign_citation":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC/action/citation_signature","submit_replication":"https://pith.science/pith/ND35BVDQYCWQQC7KBD6MBW47NC/action/replication_record"}},"created_at":"2026-05-17T23:53:34.395285+00:00","updated_at":"2026-05-17T23:53:34.395285+00:00"}