{"paper":{"title":"K-theory of Gieseker variety and type A cyclotomic Hecke algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Equivariant K-theory of Gieseker varieties equals the Jucys-Murphy center of the cyclotomic Hecke algebra over the K-theory of a point.","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Pavel Shlykov, Rapha\\\"el Paegelow, Vasily Krylov","submitted_at":"2026-05-12T06:04:09Z","abstract_excerpt":"We give an algebraic description of the equivariant K-theory of Gieseker varieties. Our main result identifies the equivariant K-theory of the Gieseker space with the Jucys--Murphy center of the cyclotomic Hecke algebra, over the equivariant K-theory of a point. The construction is inspired by the proof of the Hikita--Nakajima conjecture for Gieseker spaces given by the first and third authors. We discuss consequences for the center of cyclotomic Hecke algebras and for specializations to q=1 and to roots of unity. In particular, we relate K-theory of affine type A quiver varieties with the cen"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our main result identifies the equivariant K-theory of the Gieseker space with the Jucys--Murphy center of the cyclotomic Hecke algebra, over the equivariant K-theory of a point.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Assuming an identification between the equivariant K-theory of the Lagrangian subvariety and the cocenter (used for the roots-of-unity case).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The equivariant K-theory of Gieseker varieties is identified with the Jucys-Murphy center of the cyclotomic Hecke algebra over the K-theory of a point.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Equivariant K-theory of Gieseker varieties equals the Jucys-Murphy center of the cyclotomic Hecke algebra over the K-theory of a point.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"acd2534d615f35eeab676be990c07535188d26ceb6faf25382012ceedc866c45"},"source":{"id":"2605.11579","kind":"arxiv","version":2},"verdict":{"id":"657ba60b-3613-44ee-8389-a93cb48e93c8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T01:27:14.228339Z","strongest_claim":"Our main result identifies the equivariant K-theory of the Gieseker space with the Jucys--Murphy center of the cyclotomic Hecke algebra, over the equivariant K-theory of a point.","one_line_summary":"The equivariant K-theory of Gieseker varieties is identified with the Jucys-Murphy center of the cyclotomic Hecke algebra over the K-theory of a point.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Assuming an identification between the equivariant K-theory of the Lagrangian subvariety and the cocenter (used for the roots-of-unity case).","pith_extraction_headline":"Equivariant K-theory of Gieseker varieties equals the Jucys-Murphy center of the cyclotomic Hecke algebra over the K-theory of a point."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.11579/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-21T01:01:33.604087Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T16:56:35.643191Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-20T04:02:00.529032Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T12:33:37.950657Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"55f1c2e3f22162c106b972941c9165995cc7a366f7343d431f34d8f477023dbf"},"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"}